UNIVERSITY  OF  CALIFORNIA 
AT  LOS  ANGELES 


UNIVERSITY  of  CALIFORNIA 

AT 
LOS  ANGELES 


r  mrt  A.  n^^  . 


1^ 


STATISTICS 

IN 

BUSINESS 

THEIR  ANALYSIS,  CHARTING  AND  USE 


BY 
HORACE  SECRIST,  Ph.  D. 

PBOFBSSOB  OF  ECONOMICS  AND  STATISTICS,  N0RTHWB8TEBN 
UNIVBR8ITT,  AND  DIRECTOR  OF  THE  BUREAU  OF  BUSINESS 
RESEARCH,  NORTHWESTERN  UNIVERSITY  SCHOOL  OF  COMMERCE 
FORMERLY,  STATISTICIAN,  TONNAGE  SECTION,  DIVISION  OF 
PLANNING  AND  STATISTICS,  UNITED  STATES  SHIPPING  BOARD 
author:  an  INTEODUCTION  to  statistical  METHODS 


First  Edition 
Fourth  Impression 


McGRAW-HILL  BOOK  COMPANY,  Inc. 

NEW  YORK:    370  SEVENTH  AVENUE 

LONDON:    6  4  8  BOUVERIE  ST.,  E.  C.  4 

1921 


Copyright,  1920,  bt  the 
McGraw-Hill  Book  Company,  Inc. 


PRINTED  IN  THE    UNITED   STATES    OF   AMBBICA 


THE  MAPLE  PRESS  -  YORK  PA 


MA3I 


To 

M.  A.  S. 
H.  A.  S. 
L.  H.  S. 


PREFACE 

This  volume  has  been  prepared  primarily  for 
business  executives,  although  it  is  hoped  that  it  will 
be  of  use  in  Schools  of  Commerce.  It  aims  to  present 
briefly  and  concretely  the  reasons  why  statistics 
should  be  used  in  business  analysis,  and  to  illustrate 
how  and  with  what  effect  they  may  be  applied  in  the 
solution  of  business  problems. 

The  volume  is  not  intended  to  be  a  treatise  on 
statistics.  Its  purpose  is  to  serve  as  a  handbook  for 
executives  and  others  in  responsible  positions  in  the 
application  of  business  statistics  to  problems  which 
currently  arise.  To  this  end,  the  discussion  is  of  a 
practical  character — especial  attention  being  given 
to  the  use  of  graphs  and  charts.  Both  good  and 
bad  statistical  usages  are  developed  by  means  of 
illustrations,  and  rules  are  formulated  which  will  serve 
to  guide  executives  at  each  step  in  business  analysis 
by  means  of  statistics. 

The  treatment  is  intentionally  brief.  What  is  most 
needed,  in  the  writer's  judgment,  is  a  terse,  concrete 
discussion  of  statistics  in  business  which  executives  will 
read,  and  which  will  serve  to  suggest  the  place  which 
statistics  should  have  as  a  controlling  factor  in  business 
planning.     This  need,  this  book  endeavors  to  meet. 

The  writer  is  indebted  to  his  colleagues.  Professors 
Walter  K.  Smart  and  Franklin  Bliss  Snyder,  for 
carefully  reading  the  manuscript,  and  to  Professor 
Homer  B.  Vanderblue  and  Mr.  A.  W.  T.  Ogilvie 
for  helpful  suggestions  concerning  the  apphcations  of 
statistics  in  business. 

Horace  Secrist. 

Northwestern  University, 
December  15,  1919. 

vii 


CONTENTS 

Chapter  Paob 

I.  Modern  Business  and  Fact  Analysis 1 

II.  The  Facts  of  Business 5 

III.  Recognizing  and  Securing  the  Facts 26 

IV.  Classifying  and  Tabulating  the  Facts 41 

V.  Presenting  the  Facts — Graphics 55 

VI.  Summarizing   the   Facts — Averages    and    Other 

Means 97 

VII.  Comparison  and  the  Establishment  of  Business 

Principles  and  Standards 124 

Index 131 


IX 


STATISTICS  IN  BUSINESS 

THEIR  ANALYSIS,  CHARTING  AND  USE 

CHAPTER  I 

MODERN  BUSINESS  AND  FACT  ANALYSIS 

Business,  as  known  to  the  producer,  to  the  con- 
sumer, and  to  the  public  generally,  is  personified  in 
the  merchant,  the  banker,  the  manufacturer,  the 
farmer.  Representatives  of  each  class  may  be  known 
personally,  but  as  a  whole,  business  is  seen  as  the 
impersonal  organizations  and  relations  upon  which 
production,  distribution,  and  exchange  depend. 

Some  businesses  are  small,  some  are  large.  Some 
are  the  result  of  almost  world-wide  activity  and  fore- 
sight, while  some  are  of  local  significance  and  of  limited 
outlook.  Whatever  their  size,  or  the  extent  of  their 
activities  or  influence,  they  are  the  operating  units 
through  which  the  wants  of  mankind  are  satisfied. 
They  are  individual,  partnership,  and  corporate  enter- 
prises. To  some,  they  represent  accumulated  wealth 
operating  only  as  profit  makers;  to  others,  they  are 
primarily  service  units,  providing  the  necessities,  the 
comforts,  and  luxuries  of  life.  They  are  coopera- 
tive organizations,  through  which  modern  complex 
society,  by  the  use  of  natural  resources,  labor,  and 
inventive  genius,  not  only  satisfies  its  wants,  but  also 
expresses  its  creative  faculties.     To  the  business  man, 

1 


2     ;  STATISTICS  IN  BUSINESS 

as  such,  they  are  the  organized  machinery  for  making 
profits ;  to  the  public,  as  consumer,  they  are  the  means 
of  satisfying  wants. 

Viewed  from  either  angle,  such  business  units  rest 
on  cooperation,  trust,  confidence,  and  good-will. 
Society  as  a  whole,  and  as  classified  groups,  realizes 
its  economic  life  through  them.  This  has  always 
been  so,  but  the  type  of  the  modern  business  is  differ- 
ent from  the  ancient.  Modern  industrial  life  is  com- 
plex, the  units  are  relatively  large,  the  classes  dealing 
with  them  diverse,  and  the  relations  between  them 
impersonal.  Some  of  them  must  meet  world  com- 
petition; others,  only  that  which  is  local.  But  they 
must  all  deal  with  an  increasingly  discriminating 
public,  and  with  an  intensified  competition.  Compe- 
tition applies  to  price,  service,  and  cost.  Costs  extend 
to  a  whole  world  of  commodities,  and  service  is  drawn 
from  ever  extending  areas,  and  from  an  increasingly 
independent  labor  market.  Prices  are  governed  by 
local  and  by  national  conditions,  and  the  standards 
of  service  are  progressively  severe  and  exacting. 
Modern  business  cannot  ignore  these  facts,  nor  blindly 
meet  the  issues  which  they  raise.  The  day  of  chance 
gains  and  treasure  trove  is  passing,  if  it  is  not  past. 
The  possession  and  use  of  facts  in  business  today  spell 
the  difference  between  success  and  failure.  No  longer 
is  it  enough  to  trust  to  luck  and  to  rule-of-thumb 
methods.  Economic  and  business  judgments  must 
be  based  on  facts,  properly  analyzed  and  interpreted. 
Appeal  to  force  of  custom  and  long  continued  practice 
no  longer  suffices  as  a  basis  for  an  economic  program, 
or  business  judgment.  Ours  is  the  age  of  the  concrete. 
The  reasons  for  success  or  failure  must  be  sought  in 


MODERN  BUSINESS  AND  FACT  ANALYSIS  3 

realities.  A  fool's  paradise  in  business  brings  with  it 
its  just  reward. 

So  strongly  has  the  need  for  classified  knowledge 
come  to  be  felt  by  successful  business  during  the  last 
two  decades  that  a  true  accounting  is  today  considered 
not  only  desirable,  but  indispensable  in  industry. 
There  are  some  who  still  say,  "We  keep  no  accounts, 
we  are  successful  business  men, "  but  this  tribe  is  fast 
becoming  extinct.  Accounting  has  clarified  the  oc- 
casion for  profit  and  for  loss,  and  accurately  stated 
the  amount.  Business  has  aimed  to  be  intelligent  as 
to  past  operation;  it  has  only  here  and  there  begun  to 
be  scientific  as  to  policy  and  future  activity.  A  strict 
accounting  serves  to  meet  the  problems  internally; 
statistics  or  fact  analysis  will  meet  them  generally. 

Now,  fact  analysis  is  nothing  but  an  application  of 
scientific  method.  What  does  it  imply?  Scientific 
method  in  industry  means  recognizing  facts  and  acting 
in  the  light  of  their  interpretation.  It  means  taking 
note  of  small  differences,  seeking  for  the  similarities 
and  basic  truths  which  govern  business  and  industrial 
relations,  and  being  guided  by  them.  It  means  fore- 
sight, rather  than  hindsight;  planning  rather  than 
customary  behavior.  It  means  innovation  and  change, 
if  an  impersonal  analysis  of  the  facts  suggests  them. 
It  means  fearlessness  and  respect  for  facts. 

Scientific  analysis  of  business  and  industrial  prob- 
lems requires,  first,  a  point  of  view,  and  second,  a 
method.  The  point  of  view  is  an  unconditional 
demand  for  the  truth;  the  method  is  (1)  intelligent 
observation;  (2)  impartial  analysis;  (3)  logical  infer- 
ence; and  (4)  sincere  application  of  the  conclusion 
reached  to  the  problem  to  which  the  facts  and  obser- 


4  STATISTICS  IN  BUSINESS 

vation  apply.  Business  facts  are  numerous  and  in- 
creasingly complex ;  they  are  ever  changing  in  content 
and  application.  To  know  them  requires  keen  obser- 
vation; to  secure  them,  organization;  and  to  apply 
them,  determination  and  business  integrity.  There 
is  a  science  of  business  and  industry,  the  underlying 
facts  and  principles  of  which  can  be  determined,  and 
they  must  be  applied,  if  planning  and  foresight  are 
to  take  the  place  of  guessing  and  rule-of- thumb  action. 
Business  and  industry  need  facts,  but  most  of  all 
they  need  analysis  of  facts  and  application  of  them  to 
current  problems.  Business  will  not  run  on,  but 
down,  on  the  momentum  of  customary  action.  Fresh 
and  continuous  analysis  of  facts  is  indispensable. 
The  need  is  for  an  appreciation  of  facts,  an  ability 
to  observe  truthfully  the  conditions  which  produce 
them,  and  a  determination  logically  to  use  them  in  such 
a  way  that  they  will  serve  as  rules  for  business  guidance. 


CHAPTER  II 
THE  FACTS  OF  BUSINESS 

What  the  facts  of  business  are  which  need  to  be 
recognized,  understood,  and  applied  to  business  prob- 
lems, it  is  the  purpose  of  this  chapter  to  answer.  But 
first,  the  nature  of  a  "fact"  must  be  considered.  The 
facts  which  can  be  used  scientifically  in  business  and 
industry,  must  be  commensurable.  They  must  be 
stated,  enumerated,  or  estimated  according  to  suitable 
standards  of  accuracy;  they  must  be  collected  system- 
atically for  a  definite  purpose,  and  must  be  capable 
of  being  used  comparatively.  They  are  the  raw 
material  upon  which  positive  conclusions  are  to  be 
based,  and,  therefore,  must  be  definite,  measurable 
quantities. 

When  they  exist  ready  for  use,  they  must  be  scruti- 
nized and  their  meaning  understood.  When  they  do 
not  exist  ready  at  hand,  they  must  be  collected  or 
secured  with  these  thoughts  in  mind.  How  they  may 
be  secured  and  the  tests  to  which  they  must  be  sub- 
jected, it  is  the  purpose  of  the  following  chapter  to 
explain.  It  is  the  purpose  of  this  chapter  to  describe 
briefly  the  kinds  of  facts  by  which  business  and 
industry  must  be  positively  guided. 

Business  and  industry  may  be  classified  according 
to  the  functions  which  are  performed.  From  this 
angle,  the  producing,  selling,  marketing,  transporting, 


6  STATISTICS  IN  BUSINESS 

and  credit-making  services  are  significant.  For  in- 
stance, industry  is  designed  for  production  purposes, 
Raw  materials,  finished  and  partly  finished  commodi- 
ties, find  their  way  into  the  great  maw  of  organized 
industry,  to  be  turned  out  as  finished  products,  ready 
for  consumption,  or  as  partly  finished  products,  tc 
be  turned  back  again  into  industry,  and  subjected  tc 
further  alterations,  combinations,  or  changes.  Trans- 
portation, selling,  marketing,  and  credit  extending  are 
all  incidental  to  production  and  preliminary  to  final 
consumption. 

What  detailed  facts  must  be  known  about  these 
processes,  if  they  are  to  be  intelligently  conducted? 
Socialists  and  others  characterize  competitive  indus- 
try as  wasteful,  meaningless,  and  anarchistic  in  many 
of  its  processes,  and  the  criticism  to  a  large  degree  is 
valid.  In  a  given  plant,  purpose  and  order  may 
obtain,  but  within  industry  as  a  whole,  chaos  may 
reign.  How  can  private  industry  meet  the  challenge 
of  its  opponents,  and  justify  itself  through  the  appli- 
cation of  scientific  methods? 

Production  implies  the  creation  of  commodities  and 
services  in  response  to,  or  in  anticipation  of,  demand. 
It  requires  continuous  and  uninterrupted  additions 
of  capital,  wide  and  certain  markets,  an  uninterrupted 
flow  of  raw  materials,  and  a  contented  and  industrious 
labor  force.  In  order  for  production  to  be  conducted 
intelligently,  the  contingencies  affecting  any  and  all 
of  these  factors  must  be  definitely  known  and  dis- 
counted. If  iron  or  steel  constitutes  the  basic  raw 
material  upon  which  an  industry  depends,  the  peculi- 
arities of  its  production,  the  sources  from  which  it  ia 
drawn,  its  price  determining  factors^  transportation 


THE  FACTS  OF  BUSINESS  7 

difficulties  and  facilities,  and  its  relationship  to  credit 
conditions  must  be  appreciated.  These  can  hardly 
be  known  in  detail  by  a  single  producer  for  a  single 
supplier,  but  as  reflected  in  that  indefinite,  yet  very 
real,  thing  known  as  the  market,  they  are  determin- 
able. There  are  capital,  labor,  and  credit  markets, 
and  these  the  business  man  should  know  and  be  able 
to  interpret.  Moreover,  the  conditions  governing 
transportation  and  consumption  are  patent  to  those 
who  have  eyes  to  see  and  understanding  to  appreciate. 
The  producer,  like  others  in  the  intricate  organization 
of  business  and  industry,  must  realize  the  fact  that 
economic  life  expresses  itself  in  the  basic  facts  of  crop 
production,  credit  extensions,  business  failure,  capital 
formation,  labor  satisfaction  and  distrust.  The  view 
of  the  forest,  however,  must  not  be  confounded  with 
that  of  the  trees.  The  view  points  must  be  com- 
plementary. This  is  no  less  true  for  other  types  of 
business  than  it  is  for  the  producer. 

A  more  intimate  view  of  some  business  functions  in 
relation  to  fact  analysis  will  be  of  interest.  Why  are 
goods,  either  as  raw  material  or  as  finished  products, 
imported?  How  does  the  imported  compare  with 
the  domestic  product  in  relation  to  price,  certainty 
of  supply,  costs  in  transportation,  ease  in  handling? 
How  does  it  stand  in  relation  to  substitutes  and  com- 
petitive conditions?  Why  push  export  sales?  Are 
home  markets  exhausted,  or  has  the  point  of  diminish- 
ing returns  been  reached?  Is  the  foreign  consumer 
known  as  well  as  the  domestic;  are  there  race 
prejudices,  national  peculiarities  and  trade  customs, 
which  must  be  overcome?  Have  these  been  measured, 
and  their  significance  considered  in  the  action  taken  ? 


8  STATISTICS  IN  BUSINESS 

Have  the  facts  been  determined  in  shaping  the  policy, 
or  is  the  Hne  of  action  the  customary  or  convenient 
one?  ''Look  and  see,"  is  the  perpetual  injunction 
with  which  industry  must  ever  comply. 

But  "seeing"  is  discriminating.  To  those  who  are 
business  blind,  markets,  price  policies  and  labor 
appear  as  homogeneous  phenomena  to  be  treated  by 
fixed  formulae.  The  solution  of  problems  is  thought 
to  be  automatic.  To  those  who  really  look  and  ''see," 
all  business  problems  break  up  into  numerous  phases, 
each  requiring  different  treatment  as  principles  of  psy- 
chology, social  and  labor  theories,  etc.,  are  involved. 

But  business  and  industry  may  also  be  looked  at 
from  another  angle.  In  both,  the  facts  of  labor,  for 
instance,  must  be  known.  What  wages  are  paid, 
and  why  ?  What  are  the  living  conditions  in  industry  ? 
Do  they  tend  to  foster  a  spirit  of  confidence  and  good- 
will, or  to  play  upon  and  accentuate  industrial  ill-will? 
What  are  the  sources  and  race  characteristics  of  the 
labor  force,  and  how  are  these  related  to  questions  of 
strikes,  unrest,  sabotage,  unemployment,  accidents, 
labor  turn-over?  Is  only  labor  power  secured  when  a 
changed  policy  would  guarantee  labor  interest?  Is 
industrial  good- will  or  ill-will,  capitalized? 

Other  facts,  bearing  as  intimately  as  those  connected 
with  labor  on  the  success  of  industry,  must  be  sur- 
veyed and  used.  Capitalistic  or  machine  methods 
made  modern  large-scale  industry  possible,  and  busi- 
ness is  becoming  increasingly  capitalistic;  yet  the 
possibilities  of  machine  production,  involving  round- 
about, time-consuming,  but  prolific  processes,  are 
only  faintly  realized.  How  often  today  is  the  intro- 
duction into  industry  of  capitalistic  devices  accompa- 


THE  FACTS  OF  BUSINESS  9 

nied  by  an  application  of  scientific  method,  in  order  to 
test  their  fitness,  usefulness,  and  cost?  The  hit-and- 
miss,  rule-of-thumb  method  triumphs  in  all  but  the 
largest  and  most  enterprising  industries.  The  small, 
struggling,  wasteful,  and  planless  business  still  endures. 
A  long-time  point  of  view,  accompanied  by  observa- 
tion and  experimentation  on  the  economies  of  par- 
ticular capital  devices,  is  not  the  rule.  It  should  be, 
however,  and  undoubtedly  will  be  as  soon  as  the 
business  man  becomes  keenly  alive  to  the  logic  of 
facts  and  the  significance  of  planning  in  industry. 

Moreover,  capital  is  the  result  of  saving,  and  takes 
the  form  of  capital  goods,  only  through  investment. 
Does  the  modern  business  man  know  the  investment 
market?  The  public  is  not  a  homogeneous  mass 
which  absorbs  so  many  loans  or  exudes  a  certain 
capital  fund.  It  is  composed  of  discriminating  and 
differentiating  groups  reacting  differently  to  different 
conditions  of  credit,  time,  risk,  and  economic  return. 
Moreover,  the  public  does  not  respond  uniformly 
toward  all  types  of  enterprise.  To  the  conservative 
investor,  mining  stock  is  taboo;  to  the  plunger,  his 
forte.  Public  utility  securities,  under  a  given  philoso- 
phy of  regulation  and  the  laws  of  certain  states,  may 
be  considered  as  choice  investments.  Under  different 
philosophy  and  laws  they  may  be  a  drug  on  the  market. 
Does  the  business  man  know  the  principles  of  invest- 
ment, the  technique  of  security  issue,  and  the  facts 
which  give  investment  principles  validity? 

Again,  is  business  cognizant  of  the  facts,  practices 
and  policies  which  stimulate  confidence  and  trust,  and 
develop  credit  ?  Business  today  is  almost  synonymous 
with  credit,  reaching  out  into  the  fields  where  it  flows 


10  STATISTICS  IN  BUSINESS 

and  retreating  where  it  refuses  to  go.  What  creates 
it,  what  measures  it,  what  retains  it?  Only  business 
self-analysis  will  suggest  the  answers.  Failure  to 
receive  credit  brings  ruin.  Of  this  any  business  is 
certain,  yet  knowing  this,  the  conditions  which  support 
credit  are  ignored  because  of  a  frenzied  rush  for 
immediate  profits  and  a  disregard  of  underlying  prin- 
ciples and  their  analysis. 

The  commanding  single  element  in  business  is,  of 
course,  profit.  Profit  is  the  difference  between  costs 
assumed  and  prices  realized.  What  are  the  deter- 
mining factors  in  both?  Every  business  man  is 
perpetually  straining  with  them,  but  how  many  study 
scientifically  the  underlying  principles  of  price  deter- 
mination ?  Why  are  market  prices  fixed  at  the  current 
levels?  What  relations  exist  between  costs  of  produc- 
tion and  prices,  between  retail  and  wholesale  prices, 
between  the  prices  of  producers'  and  consumers'  goods, 
between  the  prices  of  complementary  goods,  between 
the  prices  of  goods  produced  under  conditions  of 
joint  cost?  What  is  the  elasticity  of  a  given  market? 
What  pressure  will  it  stand?  Is  it  equally  elastic  at 
all  points,  and  for  all  goods?  How  high  can  a  price  be 
before  it  reduces  sales ;  how  low  must  it  be  to  stimulate 
them?  What  latent  buying  power  is  there  and  where 
does  it  exist? 

Kule-of-thumb  methods  and  customary  behavior 
will  not  answer  these  questions,  but  the  application  of 
scientific  method  will.  Fact  analysis  in  business  and 
industry  makes  planning  intelligent.  It  gives  a  sub- 
stantial basis  for  constructive  judgments.  Business 
under  such  circumstances  is  not  enshrouded  by  a  halo 
of  obscurities,  nor  fettered  by  a  web  of  indefensible 


THE  FACTS  OF  BUSINESS  11 

practices.  It  is  still  conducted  for  profit;  it  still 
renders  service,  and  appeals  for  industrial  and  popular 
good-will,  but  it  has  incorporated  iur  itself  the  spirit 
of  scientific  method. 

It  is  unnecessary  to  show  how  the  need  for  fact 
analysis  extends  to  other  aspects  of  business.  To 
the  reader  who  has  caught  the  meaning  and  spirit  of 
scientific  method,  simply  to  enumerate  a  few  of 
these  will  suffice  to  call  his  attention  to  its  further 
application.  Costs,  prices,  public  restrictions,  and 
scientific  uses,  all  apply  to  land,  both  as  a  factor  in 
production  and  as  a  marketable  commodity.  Values 
for  taxes  may  differ  from  values  for  industrial  uses. 
The  principles  governing  rents  and  tax  capitalization 
offer  a  broad  field  for  business  research.  Are  taxes 
shifted,  and  if  so,  what  are  the  results  due  to  cost, 
public  discontent,  and  the  distribution  of  economic 
burden?  What  are  the  relative  advantages  of  land 
and  capital  goods  under  different  conditions  of  busi- 
ness growth  and  decline;  different  conditions  of  costs 
of  production  and  tax  policies? 

The  results  of  business  activities  are  revealed  in  the 
amount  of  profit;  in  industrial  growth  and  decline; 
in  the  facilities  for  exchange;  and  in  transportation  and 
industrial  and  social  well-being  and  discontent. 
Profits  must  be  studied  and  the  reality  of  them  de- 
termined. Real,  must  not  be  confused  with  paper, 
profits.  Profits  must  be  thought  of  both  from  the 
short-  and  the  long-time  points  of  view.  Failure  ade- 
quately to  provide  for  depreciation  and  o^bsolescence 
may  give  immediate  gains  but  ultimate  loss.  What 
is  a  reasonable  and  conservative  depreciation  rate? 
Analysis  of  operation  will  determine.     The  rate,  we 


12  STATISTICS  IN  BUSINESS 

may  be  sure,  will  be  different  for  different  properties 
and  for  different  conditions  of  operation,  but  the 
amount  cannot  be  divined  in  some  occult  manner,  nor 
left  as  a  "detail"  to  take  care  of  itself. 

The  amount  of  profit  and  the  business  outlook  may 
suggest  retrenchment  or  development.  Where  shall 
it  be  made?  Costs  are  not  generally  uniform,  nor  are 
profits  the  same  on  all  goods  produced  or  sold.  The 
results  of  contraction  or  expansion  may  be  satis- 
factory as  to  costs,  but  ruinous  as  to  profits.  The 
market  may  be  spoiled  by  additional  goods,  and  costs 
persist  in  spite  of  curtailed  production. 

Business,  although  competitive,  is  also  cooperative. 
One  producer  satisfies  the  demand  of  another.  Trade 
is  more  than  economic  rivalry.  The  gain  to  one  is  not 
a  loss  to  the  other.  To  satisfy  economic  wants  is  the 
goal  of  all  industrial  enterprise,  and  economy  and  the 
scientific  point  of  view  suggest  that  a  spirit  of  live  and 
let  live  should  characterize  industry.  The  truth  must 
be  known,  whether  it  applies  to  questions  of  industrial 
technique,  to  matters  of  industrial  relations,  or  to  any 
other  economic  fact.  The  more  broadly  knowledge  is 
disseminated,  and  the  more  general  the  scientific 
frame  of  mind  becomes,  the  more  nearly  will  economic 
waste  and  friction  be  dissipated  and  human  welfare 
maintained. 

Industrial  growth  today  is  determined  by  the  busi- 
ness man.  His  responsibilities  to  society  are  large 
and  his  opportunities  great.  If  he  accepts  the  scien- 
tific approach  to  his  problems,  is  fearless  enough  to 
scrap  his  prejudices,  and  at  the  same  time  construc- 
tive enough  to  observe  the  facts;  if  he  reaches  impar- 
tial conclusions  on  the  basis  of  the  facts,  and  then 


THE  FACTS  OF  BUSINESS  13 

applies  them  honestly  to  his  problems,  one  need  have 
no  fear  in  leaving  the  directive  power  in  his  hands. 
If  he  is  timorous,  cringing,  intellectually  inert,  and 
oblivious  to  the  facts  of  industry,  then  industrial 
society  must  be  recreated. 

An  outline  view  of  the  facts  with  which  the  busi- 
ness executive  must  be  familiar,  and  the  meaning  and 
application  of  which  he  must  sympathetically  under- 
stand, is  given  below.  No  attempt  is  made  to  contrib- 
ute a  complete  catalog,  nor  to  furnish  a  classification 
which  wdll  meet  all  of  the  needs  of  every  business,  but 
only  to  supply  under  classified  heads  the  outstanding 
and  basic  facts  of  business. 

Labor  Facts: 

Wages,  wage-rates  and  earnings. 

Hours. 

Union  membership,  and  types. 

Strikes  and  lockouts 

Accidents. 

Compensation,  Industrial  and  Health  Insurance. 

Unemployment. 

Turn-over. 

Immigration. 

Capital  Facts: 
Capitalization. 
Resources. 
Earnings. 

Production  Facts: 
Agricultural  crops. 
Raw  materials  extracted. 
Manufactures. 
Stocks  on  hand. 

Population  Facts: 

Geographical  distribution. 

Occupations. 

Earnings. 


14  STATISTICS  IN  BUSINESS 

Market  Facts: 
Money. 
Banking. 
Credit. 
Trade. 

Commodity  prices. 
Security  prices. 
Competition. 
Failures. 
Forecasting. 

Land  and  Building  Facts: 
Land  and  building  values. 
Taxes. 
Restrictions  on  use. 

Transportation  Facts: 
Foreign  rates  and  fares. 
Foreign  facilities. 
Domestic  rates  and  fares. 
Domestic  facilities. 
Domestic  control. 

Law  and  Policy  Facts,  as  expressed  through  law  and  the  activi- 
ties of 
State  Railroad  and  Utility  Commissions. 
State  Tax  Commissions. 
State  Industrial  Commissions. 
Federal  Trade  Commission. 
United  States  Department  of  Agriculture. 
Unted  States  Geological  Survey. 
Interstate  Commerce  Commission. 
United  States  Tariff  Commission. 

It  is  not  enough,  however,  simply  to  appreciate  that 
these  facts  have  business  significance.  It  is  necessary 
to  know  where  the  data  bearing  on  each  of  the  various 
subjects  may  be  secured,  to  know  something  of  their 
peculiarities,  and  to  be  able  to  use  them  in  connection 
with  the  problems  which  currently  arise. 

The  following  bibliographical  comments  have  refer- 
ence only  to  the  major  sources  of  business  facts,  and  to 


THE  FACTS  OF  BUSINESS  15 

some  of  the  more  evident  criticisms  which  might  be 
made  of  them.  Both  the  sources  and  the  cautions 
are  significant  more  as  a  general  than  as  a  detailed 
statement. 

Labor  Facts 

For  business,  as  a  whole,  no  single  source  of  data  on 
labor  facts  is  superior  to  the  publications  of  the  United 
States  Bureau  of  Labor  Statistics,  and  no  single  publi- 
cation of  this  bureau  is  more  significant  than  the 
Monthly  Labor  Review.  This  publication  contains 
literally  a  mine  of  information,  discriminately  col- 
lected and  issued  in  such  form  as  to  meet  many  of  the 
needs  of  business  with  respect  to  general  and  detailed 
labor  facts. 

Wage-rates  and  Earnings. — Particularly  is  the 
above  publication  significant  in  the  presentation  of 
wage  and  wage-rate  data  for  the  larger  industries,  and 
for  union  labor.  The  wage  and  wage-rate  data  are  as 
nearly  comparable  as  they  can  be  made  for  different 
times  and  for  different  types  of  enterprises.  They  are 
supplied  not  only  in  the  form  of  actual  rates,  in 
which  distinction  is  made  for  regular,  overtime,  and 
specialized  conditions,  but  are  reduced  to  a  compara- 
tive or  index  number  basis,  so  as  to  be  of  service  for 
historical  comparisons.  The  publication  does  not 
regularly  contain  wage-rates  for  non-union  labor. 
However,  from  time  to  time,  wage  data  are  given  on 
non-union  employees,  and  from  them  a  comparative 
picture,  at  least  for  a  few  industries,  may  be  secured. 

Union  Membership  and  Types. — The  Monthly 
Labor  Review,  reports  of  the  New  York  Industrial  Com- 
mission, and  the  Annual  Report  of  the  Proceedings  of 


16  STATISTICS  IN  BUSINESS 

the  American  Federation  of  Labor  contain  data  on  union 
membership,  types  of  organization,  union  agreements, 
and  other  union  activities. 

Strikes  and  Lockouts. — Similarly,  data  on  strikes 
and  lockouts  are  published  in  the  Monthly  Labor  Re- 
view. The  data  are  secured,  for  the  most  part,  from 
union  secretaries  and  others  who  are  in  a  position  to 
know  the  facts,  and  are  reduced  to  a  comparable 
basis  for  important  industries  and  for  great  industrial 
centers. 

Accidents. — Statistics  of  industrial  accidents  are 
also  published  in  the  Monthly  Labor  Review,  in  a  com- 
prehensive way,  through  special  studies  growing  out 
of  the  Bureau's  surveys,  and  in  compilations  of  acci- 
dent experience,  as  reflected  in  hazardous  industries. 
The  steel  industry  has  been  given  particular  atten- 
tion in  this  respect.  Moreover,  the  Review  regularly 
summarizes  the  legislation  having  to  do  with  acci- 
dents and  their  compensation,  with  the  rules  governing 
the  installation  and  use  of  safety  devices,  etc. 

Compensation,  Industrial  and  Health  Insurance. 
The  Monthly  Labor  Review  regularly  contains  dis- 
cussions of  compensation,  as  well  as  industrial  and 
health  insurance,  and  gives  the  statistics  that  are 
significant  on  these  subjects.  The  business  man,  in 
these  days  of  liability  for  accidents  and  industrial  dis- 
ease, cannot  afford  to  be  unacquainted  with  these 
facts,  as  here  summarized,  and  with  the  developments 
in  these  important  industrial  fields. 

Unemployment. — From  the  standpoint  of  the  in- 
dividual, and  of  industry  as  a  whole,  unemployment 
is  a  serious  problem.  It  represents  an  economic  waste 
from  the  standpoint  of  the  person  unemployed,  and 


THE  FACTS  OF  BUSINESS  17 

is  proof  of  industrial  mal-adjustment  for  industry  as  a 
whole.  Unemployment  data,  secured  from  the  larger 
industrial  centers  and  employers,  and  from  union 
records,  are  periodically  published  in  the  Monthly 
Labor  Review.  They  serve  as  a  basis  for  measuring  the 
state  of  the  labor  market  and  the  source  of  labor  sup- 
ply. In  this  field,  the  publications  of  the  New  York 
Bureau  of  Labor  and  of  the  Massachusetts  Industrial 
Commission,  are  significant. 

Labor  Turn-over. — Labor  turn-over  in  industry  is 
a  problem  to  which  the  business  executive  is  finding  it 
necessary  to  give  more  of  his  attention.  His  success 
depends  upon  a  stable  and  industrious  labor  force,  and 
every  attempt  should  be  made  to  reduce  the  turn-over 
to  a  minimum.  A  high  labor  turn-over  figure  repre- 
sents a  loss  to  the  employer,  and  a  sacrifice  of  wages 
to  the  employee.  Standards  for  measuring  it  and  the 
experience  of  larger  industries,  are  fully  discussed  in 
the  Monthly  Labor  Review,  and  business  executives 
should  be  acquainted  with  this  treatment.  Figures 
on  labor  turn-over  are  so  susceptible  of  mis-interpreta- 
tion, and  what  constitutes  labor  turn-over  is  so  difficult 
of  measurement  in  a  form  to  be  significant,  that  the 
service  of  the  Bureau  in  digesting  experience  and  es- 
tablishing standards  for  the  measurement,  ought  not 
to  be  overlooked. 

Immigration. — The  most  important  single  source 
of  data  on  immigration  is  the  reports  of  the  United 
States  Bureau  of  Immigration.  Immigrant  labor  has 
constituted,  and  will  continue  to  constitute,  an  impor- 
tant element  in  our  labor  supply.  The  relationship  of 
immigration  to  industrial  development,  to  a  fluctuat- 
ing labor  supply,  to  turn-over,  and  problems  of  manage- 


18  STATISTICS  IN  BUSINESS 

ment,  is  so  vital  that  business  executives  must  see 
this  subject  in  its  broader  aspects,  and  attempt  to 
measure  its  application  to  their  problems  as  they  arise. 
The  facts  on  immigration  are  conveniently  summa- 
rized in  a  useful  form  for  business  in  the  Monthly 
Labor  Review. 

Capital  Facts 

The  sources  of  information  on  capital  facts  are 
numerous.  At  five-year  intervals  for  industrial  and 
manufacturing  enterprises,  the  amount  of  capital  em- 
ployed is  published  in  the  reports  of  the  United  States 
Census  Bureau.  The  data  are  only  roughly  accurate 
for  separate  industries,  but  are  significant  even  in  this 
form  as  measures  of  business  activity. 

Capitalization,  as  distinct  from  capital,  is  also  re- 
ported for  industrials,  for  railroads,  and  other  types  of 
corporations,  in  Moody's  Manual,  Poor's  Manual,  etc. 
The  data  from  these  sources  are  given  for  individual 
enterprises,  rather  than  for  industries  as  a  whole,  and 
business  should  be  thoroughly  familiar  with  them. 
Similarly,  the  capitalization  of  corporations  and  other 
forms  of  business  enterprise,  is  given  in  annual  re- 
ports, and  in  the  financial  prospectuses  issued  by 
investment  houses  at  the  time  loans  are  made  and 
securities  underwritten. 

Resources. — The  resources  of  corporate  and  other 
enterprises  are  described  in  detail  in  such  financial 
publications  as  Moody's  Manual,  Poor's  Manual,  etc. 
These  publications  should  be  on  the  desks  of  business 
executives  and  constantly  referred  to  in  matters  af- 
fecting credits,  investments,  etc. 

Earnings. — The  earnings  of  industrial  and  other 
enterprises  are,  of  course,  the  most  single  significant 


THE  FACTS  OF  BUSINESS  19 

fact  in  relation  to  business  promotion  and  success. 
Earnings,  as  reported,  are  often  deceptive.  So  much 
depends  upon  the  interpretation  of  the  term,  the  con- 
ditions under  which  the  figures  are  measured,  and  the 
periods  to  which  they  apply,  that  discrimination  is 
needed  in  the  interpretation  of  the  figures  supplied,  no 
matter  what  the  source  of  the  data  is.  For  these  facts, 
in  relation  to  industrial  enterprises,  not  especially  sub- 
ject to  public  regulation,  recourse  must  be  had  to 
financial  journals,  such  as  Bradstreet's  and  Dun's. 
For  railroads  and  public  utilities,  where  regulation  by 
state  or  federal  authority  is  the  rule,  and  where  uni- 
form systems  of  accounts  prevail,  earnings  as  pub- 
lished may  in  a  more  accurate  sense  be  considered 
authoritative. 

Production  Facts 

Crops. — The  United  States  Department  of  Agri- 
culture regularly  and  periodically  supplies  facts  con- 
cerning crop  production,  crop  condition,  crop  prices, 
etc.  Particularly  worthy  of  mention  as  bearing  on 
these  problems,  is  the  Monthly  Crop  Report.  This  re- 
port gives  estimates  for  the  main  crops  on  acreage, 
prices,  total  production,  acreage  production,  and 
similar  subjects.  Special  reports  are  periodically 
made  on  crop  production,  and  intensive  studies  are 
published  from  time  to  time  on  other  important 
agricultural  problems. 

Raw  Materials  Extracted. — The  primary  source 
of  information  on  extraction  of  raw  materials,  is  the 
Geological  Survey.  The  reports  from  this  source 
cover  oil,  iron,  coal,  etc.,  and  are  prepared  in  coopera- 
tion with  state  geological  surveys  and  producers  of 
such  commodities.     Typical  private  publications  hav- 


20  STATISTICS  IN  BUSINESS 

ing  to  do  with  metal  and  mineral  products  are  The 
Iron  Age;  The  Manufactures  Record;  The  Metal  Indus- 
try; Engineering  and  Mining  Journal;  Drugs,  Oil  and 
Paint;  Coal  Age. 

Manufactures. — The  United  States  Census  Bureau 
is  the  primary  source  of  information  on  manufactures. 
The  reports  cover  capital  invested,  raw  m<aterials  used, 
wages  paid,  number  of  employees,  etc.,  for  practically 
all  of  the  important  industries  of  the  United  States. 
A  five-year  census  is  taken,  and  reports  are  issued  by 
industries  and  by  states.  From  these  data,  bulletins 
are  published  at  intervals  so  that  it  is  possible  to  make 
an  industrial  picture  of  the  country,  and  to  measure 
the  development  which  takes  place  in  each  of  the  in- 
dustries covered.  Many  of  the  data  are  little  better 
than  carefully  prepared  estimates,  but  are  of  distinct 
service  to  business  executives  and  others  upon  whom 
the  problems  of  industry  rest.  Typical  private  pub- 
lications dealing  with  manufactured  products  are  India 
Rubber  World;  The  Leather  Manufacturer;  Fiber  and 

Fabric. 

Population  Facts 

Geographical  Distribution. — The  geographical  dis- 
tribution of  the  population  of  the  United  States  is 
shown  in  the  reports  of  the  United  States  Census 
Bureau  at  its  decennial  census.  These  data  furnish 
measures  of  population  concentration,  migration,  and 
growth,  and,  if  carefully  interpreted,  may  be  used  in 
estimating  the  buying  power  of  different  markets. 
Taken  in  connection  with  the  Bureau's  report  on  Occu- 
pations, and  the  reports  of  the  Treasury  Department 
on  internal  revenues  and  income  taxes,  and  with  the 
reports  of  the  Bureau  of  Agriculture,  these  data  may 


THE  FACTS  OF  BUSINESS  21 

serve  as  a  basis  for  sales  and  advertising  campaigns, 

for  the  study  of  the  localization  of  industry,  and  other 

industrial    purposes.     The    data    are    only  roughly 

accurate,  but  rough  accuracy  is  all  that  is  demanded 

in  this  case. 

Market  Facts 

Money. — The  facts  concerning  the  circulation  of 
money  and  the  production  of  precious  metals,  are 
contained  in  the  federal  government's  reports  issued 
by  the  Treasury  Department,  the  Comptroller  of  the 
Currency,  the  Federal  Reserve  Board,  etc. 

Banking. — Data  on  banking  activities  are  regularly 
issued  by  the  Federal  Reserve  Board  in  its  Bulletin, 
and  by  the  different  state  bank  commissioners,  and 
are  summarized  conveniently  for  the  business  man  in 
such  private  publications  as  The  Commercial  and 
Financial  Chronicle;  Dun's  Review;  Bradstreet's  and  The 
Annalist  The  resources  and  liabilities  of  the  United 
States  banks  are  included  in  the  reports  of  the  Federal 
Reserve  Board,  and  those  of  the  state  banks  in  the  re- 
ports of  the  various  state  bank  commissioners. 

Credit. — Comprehensive  facts  concerning  credit  are 
to  be  had  from  the  private  publications  named  in  the 
paragraph  above,  and  in  the  daily  press  where  market 
data  on  loans,  interest  rates,  clearings,  domestic  and 
foreign  exchange  rates,  etc.,  are  published. 

Trade. — The  most  satisfactory  source  of  trade  data 
is  the  Monthly  Summary  of  Commerce  and  Finance, 
issued  by  the  Department  of  Foreign  and  Domestic 
Commerce,  Washington,  D.  C.  In  this  publication, 
exports  and  imports  are  given  in  detail,  both  as  to 
quantities  and  as  to  value.  This  publication,  to- 
gether with  the  daily  and  other  reports  of  consular 


22  STATISTICS  IN  BUSINESS 

agents,  should  be  a  common  source  of  information  to 
which  business  men  should  turn  for  data  on  this  phase 
of  their  business  activities. 

Commodity  Prices. — Data  on  commodity  prices  are 
published  regularly  by  the  financial  journals,  such  as 
Bradstreet's;  The  Annalist;  etc.,  but  are  most  conven- 
iently and  authoritatively  compiled  by  the  United 
States  Bureau  of  Labor  Statistics,  and  published  in 
the  Monthly  Labor  Review.  This  publication  includes 
both  wholesale  and  retail  prices,  and  gives  both  the 
actual  and  relative  prices  for  goods  which  enter  into 
a  consumer's  budget,  and  into  the  process  of  produc- 
tion. This  publication  compiles  both  whoesale  and 
retail  price  index  numbers,  and,  as  nearly  as  is  possible, 
supplies  a  barometer  of  price  condition  and  change 
for  the  United  States.  Commodity  prices  are  also 
included  in  a  great  number  of  private  publications, 
such  as  The  Iron  Age;  Drugs,  Oils  and  Paints;  Fiber 
and  Fabrics. 

Security  Prices. — Security  prices  of  listed  and  un- 
listed securities,  besides  being  reported  in  the  daily 
press,  are  summarized  at  intervals  in  such  publications 
as  Bradstreet's;  Dun's;  The  Annalist;  The  Economic 
World. 

Failures. — Statistics  of  financial  and  industrial  fail- 
ures are  reported  regularly  by  Dun's  Review,  and  these 
represent  the  best  available  figures  for  the  country 
as  a  whole.  Failures  constitute  a  barometer  of  trade 
and  business  conditions,  and  are  significant  in  business 
forecasts. 

Forecasting. — Statistical  data  of  a  business  character 
are  used  as  a  basis  for  business  forecasting  by  the 
Babson  Service,  Brookmire  Service,  Moody  Service  and 


THE  FACTS  OF  BUSINESS  23 

Harvard  Committee  on  EconomicResearch.  The  chief 
merit  of  the  services  issued  by  the  Babson,  Brookmire, 
and  Moody  organizations  consists,  in  the  writer's 
judgment,  in  the  great  amount  of  data  which  are 
collected,  and  which  are  made  convenient  for  business 
use,  rather  than  in  the  forecast  which  is  made.  These 
services  are  open  to  criticism  in  the  use  which  is  made 
of  the  data,  and  in  the  assumptions  which  are  made 
concerning  business  cycles;  and  should  be  used  by  the 
business  man  rather  as  a  relative  than  as  an  absolute 
measure  of  business  conditions  and  likely  change.  The 
service  now  being  issued  by  the  Harvard  Committee 
on  Economic  Research  is  thoroughly  scientific,  and 
seems  to  possess  distinct  merits  in  actual  forecasting. 
Land  and  Building  Facts. — Statistical  facts  of 
which  the  business  man  should  be  in  possession  con- 
cerning land  and  building  values,  taxation,  and  re- 
strictions on  their  use,  can  be  secured  by  a  study  of 
the  reports  of  assessors,  tax  commissioners,  and  others 
having  to  do  with  taxation  matters.  Unfortunately, 
these  facts  are  sometimes  not  available  for  business 
use,  and  in  many  instances  are  not  prepared  in  such  a 
way  that  they  are  of  distinct  service  to  business  as 
issued.  The  main  facts  are  available,  however,  even 
though  they  may  require  considerable  interpretation 
and  readjustment  for  particular  uses. 

Transportation  Facts 

Domestic  rates  and  fares  for  transportation  service 
are  regularly  published,  under  the  supervision  of  the 
federal  government,  by  carriers  and  tariff  associations. 
At  the  present  time,  the  supervision  is  exercised  by 
the  Railroad  Administration,  and  by  the  Interstate 


24  STATISTICS  IN  BUSINESS 

Commerce  Commission,  jointly.  There  is  no  occasion 
for  the  business  man  to  be  in  doubt  concerning  trans- 
portation charges,  since  the  law  clearly  requires  that 
full  publicity  shall  be  given  to  them. 

The  reports  of  the  Interstate  Commerce  Commis- 
sion on  freight  and  passenger  movements,  on  wages 
and  financial  conditions  of  transportation  companies, 
constitute  a  veritable  mine  of  information,  and  under 
the  newly  provided  accounting  system,  will  be  of  even 
more  distinct  service  than  the  reports  have  been  in 
the  past.  The  private  publications  which  most  fully 
cover  transportation  facts  are  the  Railway  Age  Gazette, 
and  Poor's  Manual,  and  the  reports  of  the  Bureau  of 
Railway  Economics,  Washington,  D.  C. 

Law  and  Policy  Facts  as  Expressed  Through  Law, 

AND  THE  Activities  of  State  and  Federal 

Boards  and  Commissions 

The  results  of  the  operations  of  public  utility  com- 
missions, and  other  state  and  federal  boards,  are  cur- 
rently summarized  in  their  annual  reports.  These 
reports,  moreover,  contain  suggested  laws,  legal  inter- 
pretations, restrictions,  and  methods  of  control,  with 
which  the  business  man  should  be  familiar,  and  which 
are  fundamental  to  his  success.  These  commissions 
have  to  do  with  railroad  and  utility  companies,  tax 
methods  and  measures,  industrial  compensation, 
health  and  accident  insurance,  wages,  trade  activi- 
ties, combinations,  competition  and  business  practices, 
tariffs,  etc. 

The  attitude  of  the  government  toward  types  of 
business  and  the  methods  which  are  followed,  should 


THE  FACTS  OF  BUSINESS  25 

be  known,  so  far  as  is  humanly  possible.  No  condi- 
tion is  so  detrimental  to  business  as  uncertainty. 
Public  opinion,  so  far  as  it  has  been  crystallized,  may 
often  be  read  in  these  reports,  and  the  business  man 
must  be  familiar  with  them. 

It  is  not  intended,  of  course,  that  every  business 
executive  should  be  familiar  with  all  of  the  facts 
suggested  above,  or  the  sources  from  which  they  may 
be  secured,  but  it  is  necessary,  in  so  far  as  the  problems 
of  his  business  extend  into  the  fields  mentioned,  that 
these  and  other  sources  of  information  should  be 
thoroughly  known,  and  the  data  which  they  contain 
be  fully  understood. 

Many  of  the  facts  which  are  needed  by  business,  in 
order  to  approach  its  problems  in  a  scientific  manner, 
are  available  in  such  sources  as  those  listed  above; 
others  are  in  process  of  collection;  and  others  must 
be  secured  de  novo.  Where  these  facts  are,  how  good 
they  are,  and  the  methods  by  which  they  may  be 
secured,  are  discussed  in  the  following  chapter. 


CHAPTER  III 
RECOGNIZING  AND  SECURING  THE  FACTS 

The  statement  was  made  in  the  beginning  of  the 
last  chapter  that  a  business  fact,  in  order  to  be  used 
as  the  basis  for  a  business  judgment,  must,  among 
other  things,  be  definite  and  measurable.  In  this 
chapter  this  point  of  view  is  given  definite  application, 
and  its  importance  illustrated  by  reference  to  con- 
crete problems. 

Every  business,  large  or  small,  is  daily  confronted 
by  a  series  of  problems.  Some  of  these  are  current, 
others  are  periodic.  About  the  solution  of  them  there 
is  often  a  degree  of  uncertainty,  which  on  the  surface 
is  baffling.  Deeper  down,  however,  many  of  them 
may,  on  investigation,  be  found  to  rest  upon  a  rela- 
tively few  major  issues,  and  group  themselves  about 
a  few  basic  facts.  Their  solution  may  in  part  be 
accomplished  by  a  proper  approach.  The  problems 
may,  for  instance,  relate  to  the  advisability  of  begin- 
ning a  campaign  of  advertising,  of  increasing  a  labor 
force,  of  more  thoroughly  cultivating  certain  sales 
territory,  as  an  alternative  to  lowering  prices,  or  re- 
adjusting production  methods,  in  view  of  increased 
wages  and  shorter  hours.  In  what  frame  of  mind 
must  the  busines  man,  no  matter  how  large  or  how 
small  a  business  he  controls,  meet  them?  What  must 
be  his  attitude  toward  them?  It  cannot  be  one  of 
inattention  and  disregard.     Problems  have  a  way  of 

26 


RECOGNIZING  AND  SECURING  THE  FACTS         27 

becoming  cumulative,  and  to  defer  them,  or  to  leave 
them  to  self-adjustment  and  self-settlement,  is  ruin- 
ous in  the  end. 

Every  business  problem  should  be  approached  by 
an  executive  with: 

First,  a  clear  and  certain  respect  for  the  truth; 
second,  a  desire  to  understand  the  facts  and  to  apply 
them  whole-heartedly  toward  a  solution  of  the  prob- 
lems. The  first  involves  a  point  of  view;  the  second, 
a  method  of  procedure. 

The  first  two  chapters  have,  we  hope,  established 
the  necessity  for  the  application  of  the  scientific 
method  to  business  problems.  So  much  for  the 
point  of  view.  It  can  now  be  taken  for  granted,  and 
the  discussion  proceed  at  once  to  the  conditions 
which  govern  its  application. 

A  business  fact,  statistical  or  otherwise,  is  always 
relative.  ''Success"  is  not  absolute;  neither  is  "fail- 
ure." ''Bumper"  crops,  "poor"  trade,  "bull"  mar- 
kets, "successful"  advertising,  "high"  interest  rates, 
and  "steady"  markets,  are  relative  expressions.  The 
statistical  data  which  express  them,  although  definite, 
are  not  to  be  interpreted  in  an  absolute  sense.  The 
measurements  are  relative  and  must  be  appraised  in 
connection  with  the  problems  and  the  conditions  to 
which  they  apply.  The  relation  between  a  problem  and 
its  measurement  is  reciprocal;  the  fact  ought  not  to  be 
divorced  from  the  problem,  and  the  problem  cannot 
be  understood  without  the  fact.  The  following  ex- 
amples of  statistical  facts,  considered  in  connection 
with  concrete  problems,  will  illustrate  the  meaning 
of  this  truth  in  business  affairs. 

A  strike  is  a  statistical  fact.     It  is  commensurable 


28  STATISTICS  IN  BUSINESS 

and  may  be  stated  numerically,  as  twenty  during  the 
year.  But  not  all  strikes  are  identical.  They  differ 
as  to  the  number  of  laborers  and  others  affected,  size 
of  industry  involved,  duration,  grievance,  temper  of 
strikers,  issues  at  stake,  etc.  The  amount  of  gross 
sales  in  dollars  is  another  statistical  fact.  But  two 
sales  experiences  of  equal  gross  amount  may  be  differ- 
ent in  every  other  respect.  One  may  result  from  an 
intensive  campaign  of  advertising  among  small  towns 
in  an  old  field;  the  other,  from  the  practice  of  direct 
selling  in  virgin  fields,  with  an  entirely  different  sales 
otganization. 

An  industrial  accident,  likewise,  is  a  statistical  fact, 
but  its  meaning  is  different  for  different  industries, 
size  and  nationality  of  labor  force,  industrial  hazard, 
conditions  of  operation,  duration  of  exposure,  etc. 
The  experience  of  the  industries  of  one  state,  as 
reflected  in  the  number  or  result  of  accidents,  is  of 
little  value  in  another  state  unless  the  basis  of  enu- 
meration is  uniform  and  the  duration  of  exposure  is 
expressed  in  a  common  unit.  The  same  is  equally 
true  in  comparing  accident  frequency  and  accident 
severity  rates  in  two  departments.  Most  of  the 
statistics  of  labor  turn-over,  when  removed  from  the 
particular  plant  or  industry  in  which  they  are  collected, 
are  of  little  comparative  value.  Units  of  measure- 
ments are  not  abstract;  they  refer  to  definite  and 
measurable  things.  A  ton,  for  instance,  is  invariably 
a  ton;  but  all  tons,  except  as  to  weight,  are  not  the 
same.  The  problem  of  enumeration  is  not  so  much 
that  of  counting  the  same  thing,  as  it  is  of  counting 
different  things  which  are  given  the  same  general 
name;  things  which  are  equal  to  each  other  in  name 


RECOGNIZING  AND  SECURING  THE  FACTS         29 

are  often  not  so  in  use.  Facts  must  be  standard- 
ized, and  standardization  implies  homogeneity;  it 
suggests  suitability  to  conditions  required  in  the  light 
of  particular  application.  The  meaning  of  a  business 
fact  is  a  function  of  the  use  to  which  it  is  put. 

The  point  which  is  being  made  is  that  the  meaning 
and  use  of  business  facts  cannot  be  dissociated.  The 
scientific  method  requires  that  problems  be  broken  up 
into  their  various  parts,  that  these  be  measured  by 
homogeneous  units,  and  that  comparisons  rest  upon 
common  qualities.  Comparisons  are  invalid,  and 
fact  analysis  useless  for  business  purposes  in  the 
degree  to  which  this  truth  is  ignored. 

The  tests  by  which  a  fact  may  be  appraised  as  a 
basis  for  a  business  judgment,  are  suggested  by  the 
uses  to  which  they  are  to  be  put.  If  crude  compari- 
sons only  are  wanted,  imperfect  facts  will  suffice. 
Trade  buoyancy  may  be  measured  for  general  pur- 
poses by  the  amount  of  exports,  imports,  or  bank 
clearings,  or  by  orders  for  steel  or  some  other  basic 
commodity.  But  individual  business  policies,  and 
the  way  in  which  they  should  be  adjusted  to  meet 
specific  problems,  can  hardly  be  based  upon  such 
general  figures.  Not  that  it  is  unimportant  in  busi- 
ness to  understand  trade  movements  and  to  observe 
the  fundamental  tendencies  in  trade,  finance,  labor 
and  production.  All  these  are  significant,  but  how 
fully  an  individual  business  may  profit  or  suffer  from 
them  can  be  determined  only  by  a  business  analysis 
of  the  particular  problems  with  which  it  is  concerned. 
A  nicety  of  discrimination  is  required  both  in  diag- 
nosing particular  business  ailments  and  in  prescribing 
the  remedies  for  them.     Only  rarely  can  business 


30  STATISTICS  IN  BUSINESS 

judgments  safely  rest  on  crude  approximations. 
Business  is  being  conducted  on  narrow  margins  of 
profits.  The  source  of  profits,  the  responsiveness  of 
customers  to  price  policies,  and  the  ways  in  which 
cooperation  and  interest  on  the  part  of  labor  may  be 
secured  can  be  determined  only  through  business 
analysis.  Analysis  involves  comparison,  and  com- 
parison requires  the  establishment  and  use  of  standards. 
These  can  rarely  be  of  a  general  character. 

Without  attempting  here  to  set  up  standards 
for  specific  types  of  business  facts,  since  each  fact 
must  be  interpreted  in  connection  with  the  prob- 
lem to  which  it  relates,  it  may  be  helpful  to  enu- 
merate briefly  the  conditions  which  are  of  universal 
application. 

As  a  basis  for  comparison  and  application  of  scientific 
method,  statistical  facts  must,  first,  be  homogeneous. 
Characteristics  which  are  significant  for  the  purposes 
for  which  the  facts  are  to  be  used,  should  not  be 
ignored.  For  instance,  men  and  women  should  be 
differentiated  in  wage  comparisons;  town  and  city 
population,  in  developing  sale  campaigns;  religious 
persuasions,  frequently,  in  estimating  buying  power. 
To  consider  a  market  without  distinguishing  con- 
sumers' buying  power,  their  personal  peculiarities  or 
their  incomes  would  be  equivalent  to  treating  as  homo- 
geneous that  which  is  clearly  diversified.  Differences 
of  training,  psychological  behavior,  standards  of 
livelihood  and  tastes  are  all  significant  in  shaping 
selling  policies.  People  are  homogeneous  as  to  com- 
paratively few  characteristics.  The  business  man 
who  conceives  of  his  problems  scientifically  will  take 
note  of  all  differences  which  are  significant  from  the 


RECOGNIZING  AND  SECURING  THE  FACTS         31 

point  of  view  from  which  he  proceeds.  Comparisons 
between  the  turn-over  of  goods  may  be  misleading  if 
this  requirement  is  forgotten.  The  turn-over  figure 
for  one  type  of  merchandise  can  not  be  accepted  for 
another.  The  market  price  which  would  discourage 
sales  in  one  field  acts  as  no  deterrent  in  another. 
Labor,  too,  is  non-homogeneous.  In  a  general  labor 
turn-over  figure  are  represented  casual  and  responsible 
labor  services.  To  replace  some,  costs  are  negligible; 
to  replace  others,  costs  are  prohibitive.  Comparisons 
must  be  made  between  things  having  common  qualities, 
regard  always  being  had  to  the  purposes  in  mind. 
Violation  of  this  principle  leads  to  imperfect  generali- 
zations and  false  conclusions. 

Second,  statistical  facts  must  be  representative.  Un- 
representative facts,  due  either  to  ignorance  or  to 
conscious  design,  are  an  uncertain  basis  upon  which 
to  base  a  business  judgment.  Where  bias  rules,  the 
occasion  for  error  exists.  When  the  motive  to  deceive 
is  present,  little  difficulty  is  encountered  in  making  a 
case.  Bias  may  be  due  to  wilfully  eliminating  part 
of  the  facts,  to  basing  conclusions  on  insufficient  data, 
or  to  comparing  periods  or  conditions  that  have  noth- 
ing in  common.  Truth  is  desired,  and  every  effort 
must  be  made  to  attain  it.  It  is  the  function  of  the 
facts  to  reveal  truth,  not  to  conceal  or  distort  it. 

In  market  analysis  by  sampling,  the  question  is 
always  important :  Are  my  samples  representative  or  is 
there  bias  running  through  them  due  to  selecting  too 
narrow  a  territory,  too  small  a  group  or  too  restricted 
a  class?  Statistical  principles  require  that  every 
sample  must  contain  the  characteristics  of  the  group 
and  that  these  be  represented  in  proportion  to  their 


32 


STATISTICS  IN  BUSINESS 


presence  in  the  original  data.  Cost  of  living  data 
selected  from  one  economic  strata  will  hardly  suffice 
to  determine  a  disputed  wage  adjustment  for  another 
group  whose  incomes  are  different.  For  instance,  the 
amount  and  per  cent,  of  expenditure  for  food  for 
12,096  white  families  in  92  industrial  centers  varies 
for  each  income  group  as  follows  :^ 

Table  1. — Amount  and  Per  Cent,  of  Expenditures  for  Food  bt 
Income  Groups 


Income  groups 

Number  of 
families 

Equivalent 
adult  males 

Average  yearly  expenditure 
for  food 

Amount 

Per  cent. 

Total 

12,096 

3.33 

$548.50 

38.2 

Under  $900 .  .  . 
$900    to  1200. . . 
1200  to  1500. . . 
1500  to  1800... 
1800  to  2100... 
2100  to  2500... 
2500  and  over . . 

332 
2,423 
3,959 
2,730 
1,594 
705 
353 

2.89 
2.98 
3.16 
3.36 
3.62 
4.09 
4.95 

371.61 
456.16 
515.55 
571.75 
626.52 
711.86 
859.98 

44.1 
42.4 
39.6 
37.2 
35.7 
34.6 
34.9 

And  yet,  is  it  not  a  common  practice  not  only  to 
ignore  the  relationship  of  expenditure  to  income,  but 
also  to  identify  expenditures  for  food,  rent,  clothing, 
etc.,  with  the ''cost  of  living"  to  any  group  irrespective 
of  the  standard  which  they  maintain?  How  com- 
pletely is  the  "cost  of  living"  represented  in  the  retail 
price  changes  of  the  22  commodities  used  by  the 
United  States  Bureau  of  Labor  Statistics?  ''Cost  of 
living ' '  to  whom  ?    Ho  w  representative  of  market  con- 

1  Monthly  Labor  Review,  United  States  Bureau  of  Labor  Statistics, 
August,  1919,  p.  118. 


RECOGNIZING  AND  SECURING  THE  FACTS         33 

ditions  are  the  25  wholesale  price  changes  weekly 
shown  by  the  New  York  Annalist? 

Again,  how  nearly  is  the  stock  and  bond  market 
gauged  by  the  average  price  of  25  industrial  stocks  or 
25  railroad  bonds?  Are  the  selected  securities  repre- 
sentative, and  what  effect  on  the  result  comes  from 
taking  an  average  (arithmetic  mean)  when  a  large 
change  in  a  single  security  may  influence  the  result  as 
much  as  minor  changes  in  a  number  of  securities? 
Moreover,  what  condition  or  personal  interests  are 
held  in  mind  in  deciding  whether  they  are  ''represen- 
tative?" Ought  not  the  prices  to  be  multiplied  by  the 
amount  sold  in  order  to  be  of  interest  to  the  speculator, 
and  multiplied  by  the  amount  outstanding  to  be  of 
significance  to  the  stockholder? 

Third,  facts  must  fit  the  problem;  they  must  be 
germane.  Do  the  facts  which  you  employ  accurately 
describe  your  problem?  Are  they  too  narrow,  or  too 
broad;  too  restricted,  or  too  general?  Are  your  prob- 
lems so  peculiar  that  the  facts  of  trade,  labor  and 
market  conditions  do  not  apply?  Why?  Can  you 
demonstrate  the  lack  of  application,  or  are  you  hiding 
behind  the  old  shibboleth,  "my  business  is  different?" 
Be  square  with  yourself,  and  scientific  toward  the 
facts  available.  If  they  do  not  fit  your  business, 
prove  it,  and  secure  those  that  do.  Ignorantly  to 
select  data  at  random  to  support  a  contention  or  to 
develop  a  business  policy  violates  both  aspects  of 
scientific  method.  There  is  then  neither  intelligent 
observation  of  facts  nor  logical  inference  from  them. 
Refer  every  fact  to  the  condition  which  can  produce  it. 

Fourth,  facts  must  be  stable.  They  must  relate  to 
periods  and  conditions  which  are  essentially  uniform. 


34  STATISTICS  IN  BUSINESS 

Look  for  the  norm  in  your  business.  Business  judg- 
ments based  on  exceptions  and  on  erratic  conditions 
or  periods  are  unstable.  Distinguish  between  the 
short-  and  the  long-time  influences,  and  in  analyzing 
your  business  difficulties,  select  the  facts  which  apply 
to  homogeneous  conditions.  Distinguish  between 
the  facts  which  measure  transitory  skirmishes  and 
those  which  describe  permanent  tendencies.  Busi- 
ness facts  are  constantly  changing;  some  fluctuate 
rapidly,  as  prices  of  speculative  securities;  others  are 
more  stable,  as,  in  normal  time,  the  rate  of  Sterling 
exchange.  Some  changes  are  sporadic;  others  are 
periodic.  When  changes  are  frequent,  measurements, 
to  be  representative,  must  be  numerous,  as  for  in- 
stance in  studying  piece-rates  in  the  clothing  trade. 
Where  periodic  changes  occur,  as  in  the  movements  of 
crops,  in  receipts  of  wheat  at  elevator  terminals,  or 
in  the  price  of  eggs,  measurements  should  cover  a  com- 
plete cycle. 

Fifth,  both  the  facts  themselves,  and  the  conditions 
of  the  measurement,  must  be  comparable.  ''Like  can 
only  be  compared  with  like."  Shifting  conditions  of 
measurement,  and  changing  units,  cannot  be  tolerated. 
Use  the  same  measuring  stick  and  apply  it  in  the  same 
way  throughout  all  measurements.  Profits  are  not 
comparable  from  period  to  period,  when  definitions 
change  and  the  base  upon  which  they  are  determined 
shifts.  Be  consistent  in  measuring  your  business 
successes  and  failures,  and  logical  in  the  interpretation 
of  them. 

Sixth,  facts  must  be  accurate.  Accuracy  is  affected 
by  the  conditions  under  which  facts  are  reported  and 
collected.     If  they  are  not  understood,  or  if  their  col- 


RECOGNIZING  AND  SECURING  THE  FACTS'        35 

lection  incites  distrust,  and  arouses  suspicion  or  the 
desire  to  protect  oneself,  inaccuracy  creeps  in.  To 
what  extent,  this  is  true,  is  often  difficult,  if  not  impos- 
sible, to  determine.  Moreover,  facts  may  be  correctly 
reported,  but  the  report  be  inaccurate  because  they 
have  been  wrongly  determined.  Occupations,  for  in- 
stance, are  confused  in  the  absence  of  standardized 
nomenclature,  and  the  real  cause  of  occupational 
death  is  often  not  revealed  because  of  amateurish 
diagnosis,  or  desire  to  conceal  the  truth.  Moreover, 
facts  may  be  inaccurate,  because  accuracy  is  impos- 
sible to  attain.  The  wages  of  farm  labor,  or  the  acre- 
age of  corn  harvested  within  the  United  States,  can 
onl}'-  be  estimated.  Estimates  are  all  that  are  desired, 
and  they  are  all  that  are  published.  Business  execu- 
tives and  others  must  treat  them  as  estimates,  and 
be  cognizant  of  the  conditions  under  which  they  are 
made.  Against  the  imputation  of  gullibility,  the 
executive  must  always  be  capable  of  defending  himself. 

The  facts  of  business  for  the  most  part  grow  out  of 
daily  routine  operations.  Some  are  collected  by 
business  organizations  for  their  own  use,  some  by 
trade  publications,  and  still  others  by  governmental 
agencies.  What  the  significant  facts  are,  which  are 
hidden  away  in  routine  reports,  or  systematically 
collected,  it  is  the  function  of  the  business  man  to 
know;  how  they  apply  to  his  problem,  it  is  his  duty  to 
understand. 

In  studying  business  facts,  the  executive  must  apply 
both  general  and  specific  tests  of  worth  and  applica- 
tion. In  searching  his  own  records  for  them,  he  must 
classify  his  problems  and  apply  the  facts  which  are 
germane.     While  business  units  operate  primarily  for 


36  STATISTICS  IN  BUSINESS 

profit,  and  only  secondarily,  if  at  all,  as  statistical 
laboratories  in  the  production  of  facts,  yet  the  rela- 
tion between  fact  analysis  and  business  success  is  so 
close  that  it  cannot  be  ignored.  Statistical  and  re- 
search departments  cannot  become  a  part  of  every 
business  undertaking,  but  there  is  no  business  so 
small  that  it  cannot  duplicate  in  a  small  but  effective 
way  the  attitude  of  mind  suggested  by  these  special 
departments.  This  attitude  is  one  of  business  curiosity 
and  intellectual  integrity  toward  problems  as  they 
arise. 

The  attitude  of  the  executive  toward  his  business 
affairs  must  be.  Why?  Where  is  the  logical  justifica- 
tion of  the  action  taken?  Does  custom  dominate 
the  contents  of  my  records,  my  reports,  my  office 
organization,  my  advertising,  the  treatment  of  my 
labor  force?  How  do  I  stand  with  my  competitor, 
in  the  matter  of  costs  and  services?  Are  the  resources 
of  my  organization  fully  employed?  How  might  I 
use  my  office,  sales,  and  production  records  to  decrease 
costs,  to  analyze  my  markets,  experiment  with  prices, 
increase  my  capital,  and  decrease  my  labor  turn-over? 
Is  my  business  a  'Agoing"  concern,  and  where  is  it 
"going?" 

Business  analysis — the  application  of  scientific 
method — -in  commercial  enterprise,  will  answer  such 
queries,  and  suggest  such  positive  action  as  the 
following:  How  can  I  extend  my  market?  (Describe 
your  present  market  in  terms  of  its  possibilities.)  Is 
my  sales  record  the  best?  (Establish  a  standard  of 
''best.")  What  are  my  selling  costs?  (Define  costs 
accurately  and  defend  the  amount.)  What  share  of 
the  business  in  my  line  am  I  getting?     (Measure  and 


RECOGNIZING  AND  SECURING  THE  FACTS         37 

localize  the  buying  power  available. )  Are  my  salesmen 
the  best?  (Establish  a  standard  of  salesmanship  and 
realize  it  in  your  own  organization.)  Are  the  reports 
of  my  salesmen  filled  with  business  meaning,  or  are 
they  perfunctory?  (Submit  them  to  critical  inspec- 
tion, and  make  yourself  defend  them.) 

A  business,  to  be  successful,  must  have  standards 
and  be  critical  of  them;  it  must  eliminate  the  dry  rot 
which  unconsciously  accumulates,  and  accept  the 
truth,  that  progress  means  change,  but  change  only  as 
the  result  of  conscious,  purposeful  choice.  Beware 
of  innovations  as  such — the  gold  bricks  of  success — ■ 
but  welcome  and  cultivate  improvement  through 
positive  change. 

The  facts  which  are  needed  for  the  solution  of  many 
business  problems  exist  in  whole,  or  in  part,  in  the 
daily  records  which  are  kept.  When  they  are  not 
currently  collected,  they  must  be  secured.  It  may  be 
necessary  in  large  establishments  to  create  separate 
departments  to  secure  and  interpret  them;  in  others 
it  may  require  nothing  more  than  the  interest  and 
talents  of  a  single  individual.  Business  does  not 
hesitate  to  adopt  the  specialized  machinery  of  produc- 
tion; it  must  not  hesitate  to  install  suitable  machinery 
for  the  collection  and  interpretation  of  business  facts. 
To  determine  what  these  are,  where  they  are,  how 
they  may  be  collected,  what  they  mean,  and  how  they 
may  be  applied  in  the  solution  of  business  problems, 
constitute  the  essence  of  fact  analysis. 

A  serious  weakness  of  business  is  to  allow  the 
problem  of  office  organization,  accounting  readjust- 
ments, etc.,  to  drift.  In  many  instances,  the  changes 
and    modifications    which    are    essential    to  secure 


4982'' 


38  STATISTICS  IN  BUSINESS 

economy  and  to  increase  output  are  not  known. 
This  may  be  due  to  wilful  ignorance,  or  more  often, 
probably,  among  smaller  business  units,  to  lack  of 
facilities  for  keeping  in  touch  with  modern  develop- 
ments and  progress  touching  these  matters.  The 
latter  condition,  by  means  of  advertising  and  other 
educational  methods,  will  sooner  or  later  be  dispelled 
for  all  but  a  fraction  of  establishments.  There  is  not 
so  much  hope,  however,  for  the  wilfully  ignorant — 
for  the  individual  who  ''knows  it  all,"  and  at  the  same 
time  knows  little  or  nothing  beyond  the  routine  of  his 
daily  grind.  Concerning  this  individual,  hope  lies 
primarily  not  in  education,  but  in  elimination. 
Sooner  or  later  he  must  give  way.  His  goods  and 
services,  coming  at  too  great  a  cost,  are  lost  to  the 
market,  and  justly  so.  Competition  slowly  forces 
him  out,  but  only  after  the  social  costs  have  become 
intolerable.  He  or  his  like  reappears,  however,  be- 
cause of  the  unequal  advantages  under  "which  industry 
is  carried  on — there  is  a  sort  of  perpetual  handicap 
for  some  running  throughout  all  industry.  It  may, 
however,  be  lessened  by  business  self-analysis.  Where 
the  disposition  to  make  this  analysis  does  not  exist, 
and  where  the  justification  for  not  making  it  is  sought 
in  a  self-centered  complacency,  the  problem  is  hopeless. 
More  often,  however,  lack  of  progress  is  due  not  so 
much  to  wilful  ignorance  as  it  is  to  the  absence  of  a 
scientific  approach  to  business  problems.  An  execu- 
tive may  be  open  to  suggestion;  he  may  be  willing  to 
adopt  labor-  and  time-saving  devices,  and  may  have 
caught  the  social  point  of  view  respecting  problems 
of  labor.  He  may  also  approach  market  problems 
from  the  standpoints  of  psychology  and  of  the  new 


RECOGNIZING  AND  SECURING  THE  FACTS         39 

competition  and  upon  the  basis  of  analysis  of  popula- 
tion and  occupational  data.  But  still  there  may  be 
something  lacking  in  his  attitude — something  that  is 
vital  to  the  application  of  the  scientific  method. 
What  too  many  progressive  business  executives  fail 
to  realize  is  that  the  scientific  method,  or  fact  analysis, 
is  not  to  be  applied  sporadically;  is  not  to  be  applied 
here  and  neglected  there;  begun  and  then  allowed  to 
lapse.  For  an  executive  to  appreciate  the  meaning 
of  fact  analysis  is  not  enough.  He  must  create  and 
maintain  an  organization  to  apply  it.  It  must  become 
a  religion  not  only  to  him,  but  to  the  others  in  his 
industry  as  well.  Simply  to  order  sales  to  be  analyzed, 
or  a  new  acounting  control  to  be  established,  without 
at  the  same  time  providing  the  ways  in  which  it 
shall  be  done,  and  allowing  for  all  of  the  consequences 
which  will  follow,  is  only  to  catch  a  glimpse  of  the 
meaning  of  scientific  method.  Glimpses  alone  are  not 
enough;  conviction  is  what  is  needed,  and  this  must  be 
general  and  felt  by  all  those  on  whom  responsibilities 
rest.  The  lesser  officials,  the  department  managers, 
and  even  the  workers  themselves,  are  the  ones  who 
are  in  a  position  to  see  the  need  for  fact  analysis;  and, 
if  convinced  of  its  services,  can  be  of  inestimable  ser- 
vice to  the  management  in  suggesting  improvements 
to  be  made  and  in  observing  the  results  of  the  changes 
introduced.  The  technique  of  scientific  method  will 
have  to  be  applied  by  the  expert,  but  he  should  have 
not  only  the  sympathy  but  also  the  cooperation  of  all 
those  in  whom  any  responsibility  rests.  An  esprit  de 
corps  is  indispensable. 

Scientific  method  has  been  defined  as  a  state  of 
mind,  and  this  is  probably  a  true  characterization  if 


40  STATISTICS  IN  BUSINESS 

the  condition  is  added,  that  the  point  of  view  it  repre- 
sents is  consistent  in  seeking  the  truth  and  being 
guided  by  facts  not  at  one  time,  in  one  place  or  under 
one  condition,  and  ignoring  them  when  it  becomes  ad- 
vantageous, or  when  they  are  difficult  to  determine, 
but  in  all  places,  at  all  times,  and  under  all  conditions. 
Cost  accountants,  statisticians,  and  industrial  engi- 
neers, in  the  study  of  business,  are  continually  finding 
conditions  which  are  deplorable;  where  every  princi- 
ple of  scientific  method  is  violated,  and  where  businesses 
are  running  on  without  cost  figures,  depreciation  re- 
serves, sales  analysis,  and  comparative  and  basic 
operating  data.  A  remedy  is  sought  at  the  hands  of 
the  expert,  but  only  for  certain  specific  ills,  and  not  for 
a  complete  constitutional  treatment.  Changes  are 
introduced  with  fear  and  hesitancy,  doubt  character- 
izing every  innovation. 

This  is  not  the  spirit  of  scientific  method.  To  the 
fact  analysist,  facts  are  facts.  They  are  welcomed  for 
the  truth  they  contain.  The  attitude  toward  them 
and  toward  the  changes  which  they  make  imperative, 
is  positive,  receptive,  and  open  minded;  not  negative, 
doubtful  and  hesitant.  It  is  not  a  little  truth,  but 
the  whole  truth,  which  is  wanted.  Nothing  is  too 
sacred,  too  old,  nor  too  customary  to  be  challenged. 
Truth  from  whatever  source  is  sought  out  and  wel- 
comed, and  applied  to  problems  as  they  arise. 


CHAPTER  IV 
CLASSIFYING  AND  TABULATING  THE  FACTS 

Business  analysis  involves  the  classification  of  facts, 
the  application  of  them  to  business  problems,  and  the 
formation  of  business  judgments.  The  methods  of 
classifying  facts  and  of  presenting  them  in  tabular 
form  are  treated  in  this  chapter.  The  following  chap- 
ter is  concerned  with  the  principles  and  rules  of 
graphic  presentation. 

Business  phenomena  and  the  data  bearing  upon 
them  must  be  classified.  Business  judgments  which 
call  for  more  than  nominal  consideration,  are  made 
on  the  basis  of  some  sort  of  analysis.  The  pros  and 
cons  are  considered,  given  their  appropriate  weight, 
and  a  final  determination  made.  Decisions  must  be 
reached  and  actions  taken.  Upon  what  basis  are 
decisions  made?  How  soberly  are  the  facts  consid- 
ered; is  their  use  scientific? 

Classification  consists  in  separating  facts  according 
to  a  definite  plan,  into  groups,  according  to  certain 
characteristics,  and  of  placing  them  in  tables,  and  in 
graphic  or  other  form,  for  the  purpose  of  presentation. 
It  presupposes  a  definite  knowledge  of  the  purpose 
for  which  facts  are  studied,  and  the  manner  of  pres- 
entation depends  upon  the  ease  with  which  data,  as 
classified,  may  be  understood.  Sometimes  tabula- 
tion suffices,  and  is  easily  understood.  In  other 
cases,  some  form  of  graphic  expression  is  indispensable. 

41 


42 


STATISTICS  IN  BUSINESS 


The  advantages  of  clearly  defined  and  logically 
constructed  tabulation  forms  are  many.  Tables  sys- 
tematize data  and  show  the  order  of  arrangement. 
They  make  it  possible  to  show  group  relations  and 
bring  out  comparisons.  They  facilitate  addition  and 
summarization,  and  avoid  the  necessity  of  repeating 
headings  and  of  duplicating  items.  In  short,  they  are 
a  means  of  recording  in  permanent  form  the  analysis 
that  is  made  through  classification  and  of  placing  in 
juxtaposition  things  that  are  similar  and  should  be 
compared.  How  true  this  is  may  be  seen  by  com- 
paring the  following  methods  of  showing  the  number 
of  occupational  deaths  among  cotton  mill  operatives 
in  Fall  River,  1905-1912. 

"The  recorded  number  of  male  operative  decedents  in  Fall 
River  for  the  eight-year  period  (1905-1912)  was  915.  Of  these 
233  .  .  .  were  found  not  to  have  been  cotton-mill  operatives, 
while  207,  who  on  their  death  certificates  were  assigned  to  other 
occupations,  were  really  cotton-mill  operatives  at  the  time  of 
their  death.  The  real  number  of  male  operative  decedents, 
therefore,  was  889,  the  group  as  recorded  having  been  larger  by 
26  than  the  facts  justified. 


Table    2. — Occupational   Deaths — Cotton-mill   Operatfves   in 
Fall  River  for  Period,  1905-1912 


Occupational  deaths — cotton-mill  operatives 

Male 

Female 

Total 

889 

936 

Recorded  number 

915 
-233 
207 

-26 

548 

Non-operatives  included 

-71 

Operatives  not  included 

459 

Balanced  error 

+388 

CLASSIFYING  AND  TABULATING  THE  FACTS        43 

"On  the  other  hand  the  recorded  number  of  female  operative 
decedents  in  Fall  River  for  the  eight-year  period  was  548.  Of 
these  71  .  .  .  were  found  not  to  have  been  cotton-mill  operatives, 
while  459,  who  were  recorded  either  as  having  other  occupations 
or  no  occupation  at  all,  proved  on  investigation  to  have  been 
really  cotton-mill  operatives.  This  gives  a  total  of  936  decedent 
female  operatives."  ^ 

In  order  to  tabulate  statistical  data,  they  must 
generally  be  prepared  for  this  purpose.  Sometimes 
the  units  can  be  transferred  directly  into  prepared 
tables  from  reports,  memoranda,  and  such  sources. 
In  most  instances,  however,  they  have  to  be  tran- 
scribed, rearranged,  combined,  coded,  etc.,  before 
this  process  begins.  Whether  taken  from  secondary 
sources,  or  collected  from  business  records,  they  are 
still  raw  material,  and  consistency  in  classification  is 
indispensable.  The  identity  of  the  facts  included 
must  be  as  complete  as  possible.  A  table  is  no  better 
than  the  classification  that  it  expresses. 

In  tabulating  statistical  data,  strive  for  simplicity. 
Make  tables  simple  in  outline  and  their  purpose 
evident.  Avoid  too  complex  tabular  arrangements, 
and  place  in  immediate  relationship  the  facts  which 
are  to  be  compared.  The  order  in  which  the  data 
appear  should  be  natural,  emphatic,  and  convincing. 

The  following  table  shows  the  form  in  which  the 
municipal  offerings  of  a  Chicago  investment  house 
were  distributed  to  the  public.  The  investor  is  prob- 
ably most  interested  in  the  "net"  return — notice 
the  order  in  which  the  issues  are  listed.  The  purpose 
of  the  arrangement  is  clear. 

^  Monthly  Review,  United  States  Bureau  of  Labor  Statistics,  July, 
1917,  pp.  7-8. 


44  STATISTICS  IN  BUSINESS 

Table  3. — Bonds  fok  Safe  Investment 


Amount 


Name  of  issue 


Rate 


Price 

Maturity 

and 

interest 

Nov.    2,  1934 

102.78 

Aug.    1.  1925 

103.10 

Nov.    1,  1956 

92.71 

July      1,  1939 

94.75 

Nov.    1,  1928 

103.75 

July    3,  1933 

94.92 

Feb.    1,  1920 

99.75 

Oct.  29,  1939 

100.99 

Oct.  24,  1939 

101 .30 

Oct.  29.  1939 

102.37 

July    1,  1921 

100.67 

Dec.    1,  1931 

105  .86 

Oct.  29,  1959 

101.00 

July  15,  1949 

100.00 

Oct.  29,  1949 

100.00 

1929  to  1941 

100.00 

Netting 
about 


$30,000 
60,000 
20,000 

100,000 

34,000 
20,000 
10,000 
90,000 
50,000 
100.000 
10.000 
40,000 

200.000 

200,000 

15,000 

30,000 


Buffalo,  N.  Y.,  Registered..  . 

Camden  County.  N.  J 

New  York  City.  Registered.  . 
St.  Louis.  Mo.,  Bd..  of  Ed. 

School 

Bayonne,  N.  J 

California,  State  Highway. . . 
Cook  County  Forest  Reserve 

Ogden,  Utah,  School 

Fremont,   Neb..  Refunding. . 

Pocatello,  Idaho 

Seattle.  Wash 

Miami  Conservancy  District, 

Ohio 

Polk  County,  Texas,  Road. . 
Blount  County,  Tenn.,  Road 
Denton  County,  Texas,  Road 
Hill   County,    Texas,    Road 

Diat 


4^ 

5 

4 

4 

5 

4 

4 

4?4 

5 

5 

5 

5 
5 
5 


4.25 
4.40 
4.40 


4.70 

4.85 
4.87 
5.00 
5.00 

5.00 


Contrast  the  following  tables,  so  far  as  order  of 
arrangement  is  concerned. 


CLASSIFYING  AND  TABULATING  THE  FACTS        45 

Table  4. — United  States  Crop  Estimated  Production 
August  1,  IQlQi 


Crapa 


Production 


1919 

indications, 

Aug.  1 


Com,  bushels 

Winter  wheat,  bushels 

Spring  wheat,  bushels 

All  wheat,  bushels 

Oats,  bushels 

Barley,  bushels 

Rye,  bushels 

Buckwheat,  bushels 

Potatoes,  bushels 

Sweet  potatoes,  bushels 

Flaxseed,  bushels 

Rice,  bushels 

Tobacco,  pounds 

Hay  (all),  tons 

Cotton,  bales 

Apples,  total  crop,  bushels 

Peaches,  bushels 

Pears,  bushels 

Kafirs,  etc.,  6  states,  bushels. 
Peanuts,  bushels 

Beans  (dry),  6  states,  bushels 

Sugar  beets,  tons 

Broom  corn,  5  states,  tons . . . 

Sorghum,  sirup,  gallons 

Hops,  pounds 


2,788,378,000 
715,301,000 
225,080,000 
940,381,000 

1,266,401,000 

203,525,000 

84,552,000 

16,103,000 

357,120,000 

100,456,000 

10,239,000 

43,427,000 

1,335,052,000 

110,876,000 

11,016,000 

155,004,000 
49,793,000 
12,260,000 

130,153,000 
57,547,000 

12,338,000 

6,963,000 

59,100 

33,757,000 

34,906,000 


^  Monthly  Crop  Report,  United  States  Department  of  Agriculture, 
August,  1919. 


46 


STATISTICS  IN  BUSINESS 


Table  5. — Production  of  Corn  in  the  Leading  Five    States, 

1916-19181 
(000  omitted) 


1918 

1917 

1916 

State 

Produc- 
tion 
Bushels 

Per 
cent. 

of 
U.S. 

State 

Produc- 
tion 
Bushels 

Per 
cent. 

of 
U.S. 

State 

Produc- 
tion 
Bushels 

Per 

cent. 

of 

U.S. 

U.  S. 

2,582,814 

100.0 

U.  S. 

m 

.3,065,233 

100.0 

U.  S. 
Iowa 

2,566,927 

100 

.0 

Iowa 

375,624 

14.5 

418,000 

13.6 

366,825 

14 

.3 

Ill 

351,450 

13.6 

Iowa . . . 

410,700 

13.4 

111 

300,900 

11 

7 

Ind 

169,554 

6.6 

Nebr... 

249,480 

8.1 

Nebr . . . 

192,400 

7 

5 

Mo 

133,860 

5.2 

Mo 

241,500 

7.9 

Ind 

174,658 

6 

.8 

Ohio 

133,200 

5.2 

Ind  ...  . 

5  States 

196,776 

6.4 

Mo 

5  States 

132,112 

5. 

1 

5  States 

45.1 

49.4 

45 

4 

There  is  no  particular  sacredness  about  any  order 
in  tabulation,  unless  it  is  the  alphabetical.  The  order 
should  generally  be  chosen  so  as  to  emphasize  the 
classification  which  is  adopted.  An  unnatural  or 
rule-of-thumb  arrangement  is  never  justified. 

What  seems  to  be  the  basis  of  arrangement  of  the 
details  in  Table  6,  showing  the  classification  of 
statistics  of  corporate  incomes  in  1916,  as  published 
by  the  Commissioner  of  Internal  Revenue? 

Tables  2,  above,  and  7,  following,  illustrate  what 
may,  for  convenience,  be  called  ''Progress"  tables. 

In  the  clearest  way  possible  project  onto  a  tabular 
form  the  message  which  is  wished  to  be  conveyed. 
Make  the  totals  prominent  by  placing  them  first, 
and  show  the  relative  importance  of  the  classifica- 
tion by  the  rulings  and  the  spacings  of  major  and 

^  Monthly  Crop  Report,  United  States  Department  of  Agriculture 


CLASSIFYING  AND  TABULATING  THE  FACTS        47 
Table  6. — United  States  Corporate  Income  Statistics,   1916^ 


1916  Classification 


Class 

Xet  income 

Total 

S8, 765,908, 984 

Banks 

Insurance  companies 

Public  utilities 

Extraction  of  minerals 

Manufacturing  and  mechanical. . . . 

Merchandising 

Agriculture  and  animal  husbandry . 
Miscellaneous 


400,599,580 

127,906,231 
1,541,076,130 

798,883,349 
4,157,625,900 

464,875,807 

69,862,431 

1,205,079,556 


Table  7. — Live  Stock  Changes  during  July   ^ 


Cattle 


Swine 


Sheep 


1919 

1918 

1919 

1918 

1919 

100.00 

100.00 

100.00 

100.00 

100.00 

2.78 

3.19 

7.88 

9.86 

.38 

1.53 

2.99 

1.79 

2.16 

.53 

4.97 

6.01 

8.48 

11.31 

4.80 

.29 

.49 

.30 

.45 

.44 

.34 

.45 

1.79 

1.68 

.81 

98.71 

99.23 

99.10 

98.58 

94.86 

1918 


On  farms  July  1 

Births  in  July 

Brought  on  farms  in  July 
Moved  off  farms  in  July. 
Farm  slaughter  in  July. . 
Died  on  farms  in  July. . . 
Remaining  Aug.  1 


100.00 

.38 

2.14 

5.85 

.60 

.87 

95.20 


minor  headings.  Make  tables  attractive,  concise, 
and  emphatic.  Fit  them  appropriately  to  standard 
sized  pages;  number  the  lines  and  columns  when  this 
will  result  in  clarity;  and  above  all  give  them  suitable, 

^  American  Economic  Review,  September,  1919,  p.  512. 

'  Monthly  Crop  Report,  United  States  Department  of  Agriculture. 


48 


STATISTICS  IN  BUSINESS 


brief,  but  explicit  titles.  A  title  should  be  a  concise 
epitom^  of  the  contents  of  a  table.  It  is  not  its  pur- 
pose to  include  all  of  the  facts  which  a  table  contains. 
It  should  be  short,  well  punctuated,  clearly  phrased, 
and  incapable  of  being  misconstrued.  Titles  are 
generally  faulty  because  of  omissions  and  an  inverted 
order  in  the  characteristics  which  are  named.  The 
natural  order  is  from  superior  to  subordinate  items. 

Classification  and  tabulation  generally  require  that 
the  facts  be  grouped,  or  condensed.  It  is  impossible 
to  retain  the  individuality  of  each  item.  Abbrevia- 
tion— a  sort  of  telescoping — is  necessary,  but  it  is 
also  dangerous,  because  it  sacrifices  accuracy.  Con- 
ciseness and  brevity  are  desirable  in  tables,  but  not  at 
too  great  a  sacrifice.  How  far  grouping  may  go 
depends  upon  the  problem  in  mind  and  the  occasion 
for  classification.  What  it  involves,  however  must 
not  be  ignored. 

Using  the  data  in  Table  3,  the  issues  may  be  con- 
densed as  follows,  but  the  detail  which  is  necessary 
for  viewing  the  issues  individually  is  lost. 

Table  8. — Municipal  Issues  Classified  by  Net  Interest  Rate 


Net  interest  rate,  per  cent. 

Number  of 
issues 

Amount  of 
issues 

Total 

16 

$1,009,000 

4.00  to  4.25 

4 
7 
2 
3 

4  25  to  4  50 

210,000 

4  50  to  4.75 

314,000 

4.75  to  5.00 

240,000 

5  00  and  over 

245,000 

CLASSIFYING  AND  TABULATING  THE  FACTS        49 

More  serious  for  detailed  analysis  is  the  grouping 
shown  in  the  following  table. 


Table  9. — Number  of  Income  Tax  Returns  by  Classes,  1914-19161 


$3,000-  $4,000. 

4,000-  5,000. 

5,000-  10,000. 

10,000-  15,000. 

15,000-  20,000. 

20,000-  25,000. 

25,000-  30,000. 

30,000-  40,000. 

40,000-  50,000. 

50,000-  100,000. 

100,000-  150,000. 

150,000-  200,000. 

200,000-  250,000. 

250,000-  300,000. 

300,000-  400,000. 

400,000-  500,000. 
500,000-1,000,000. 
1,000, 000-and  over. 


Incomes 

Total  number  of  returns 

1914 

1915 

1916 

Total 

357,515 

336,652 

429,401 

82,754 

69,045 

85,122 

66,525 

58,949 

72,027 

127,448 

120,402 

150,551 

34,141 

34,102 

45,305 

15,790 

16,475 

22,621 

8,672 

9,707 

12,956 

5,483 

6,196 

8,055 

6,008 

7,005 

10,068 

3,185 

4,100 

5,611 

5,161 

6,847 

10,452 

1,189 

1,793 

2,900 

406 

724 

1,284 

233 

386 

726 

130 

216 

427 

147 

254 

469 

69 

122 

245 

114 

209 

376 

60 

120 

206 

^American  Economic  Review,  September,  1919,  p.  503. 

The  distribution  of  the  items  within  the  groups  is 
concealed.  Whether  the  items  are  concentrated  at 
the  upper  or  the  lower  sides  of  the  groups,  or  are 
distributed  uniformly  through  them,  is  not  known. 

The  contents  of  tables  should  unmistakably  bear 
on  the  problems  to  which  they  relate.  Extraneous 
matter  should  be  removed.     Tables  should  be  explicit 


50  STATISTICS  IN  BUSINESS 

and  contain  a  minimum  of  ''unclassified,"  "not 
stated,"  and  "miscellaneous"  material.  If  this  type 
predominates,  it  is  either  a  suggestion  of  a  desire  to 
withhold  some  of  the  detail,  or  evidence  that  the  basis 
of  classification  is  faulty. 

The  scientific  mind  sees  things  in  groups.  It  classifies 
according  to  common  characteristics,  heterogeneous 
and  seemingly  unrelated  facts;  traces  out  similarities, 
and  looks  for  cause  and  effect.  It  seeks  underlying 
principles  through  analysis.  "Classification  is  indis- 
pensable to,  and  accompanies  every  scientific  infer- 
ence," and  tabulation  involves  far  more  than  drawing 
lines  and  inserting  numerical  symbols.  It  is  a  means 
of  recording  classification  and  analysis. 

But  how  is  a  business  to  study  its  problems  by 
means  of  tabulating  the  facts  which  it  currently 
receives?  For  most  businesses  it  is  unnecessary  to 
create  an  elaborate  organization  for  this  purpose. 
Every  business  should  provide  some  specialized 
machinery  to  scrutinize  currently  the  records  which 
are  received,  and  to  test  by  experiment  the  relation 
which  they  have  to  current  problems.  This  can  be 
done  by  tabulating  the  facts  and  by  observing  the 
underlying  principles  which  seem  to  determine  them. 
If  the  records  do  not  contain  all  the  facts  which  are 
necessary  either  to  explain  a  problem,  or  to  furnish  a 
continuing  picture  of  a  business  operation,  it  is  neces- 
sary to  seek  new  data  through  additional  records,  or 
through  schedules  sent  to  the  various  operating  divi- 
sions, or  the  groups  concerned  with  operation,  sales, 
etc.  If  additional  information  on  sales,  on  office 
methods,  on  production  costs,  are  required,  this  can 
be  secured  by  means  of  schedules,  if  they  are  properly 


CLASSIFYING  AND  TABULATING  THE  FACTS        51 

framed  so  as  to  enlist  the  support  and  cooperation  of 
those  to  whom  they  are  sent. 

The  problems  of  classifying  and  grouping  dissimilar 
facts,  of  separating  large  aggregates  into  their  several 
parts,  and  of  building  up  totals  from  details  are 
intimately  related  to  the  methods  by  which  facts  are 
collected.  Every  step  in  the  collection  process  in- 
volves some  sort  of  tabulation.  Indeed,  collection 
and  tabulation  of  facts  are  but  two  steps  in  one 
general  process  of  classification. 

There  is  a  technique  in  the  method  of  collecting 
facts  which  is  important,  and  which  business  should 
seek  to  apply.  In  every  industry,  departmental  jeal- 
ousies are  common,  sectional  points  of  view  maintain, 
and  it  is  frequently  difficult  to  overcome  them  and 
to  secure  the  united  cooperation  of  all  in  matters  of 
common  interest.  Personal  interviews  will  help  to 
pave  the  way  for  securing  information,  and  the  tone 
in  which  inquiries  are  made  will  serve  to  establish 
confidence.  Cooperation  is  indispensable,  and  any- 
thing which  will  contribute  toward  it  must  be  capital- 
ized. Above  all,  suspicion  must  be  allayed,  and 
sectional  and  narrow  personal  interests  dispelled. 

The  preparation  of  schedules  is  simple,  but  funda- 
mental principles  should  be  observed. 

First. — Assurance  should  be  given,  either  within 
the  schedule  itself  or  preparatory  to  its  being  sent, 
that  the  inquiries  are  made  for  the  good  of  the  busi- 
ness as  a  whole,  and  that  it  is  mutually  advantageous 
that  the  questions  be  answered  fully  and  accurately. 
Cooperation  must  be  solicited.  The  collection  of 
full  and  satisfactory  information  depends  upon  the 
existence   of   good- will   and    mutual   understanding. 


52  STATISTICS  IN  BUSINESS 

Second. — Schedules,  or  inquiries,  should  be  as  brief 
as  is  consistent  with  the  purposes  for  which  they  are 
intended,  and  the  questions  unmistakably  addressed 
to  the  problem  involved.  So  far  as  is  possible,  the 
relation  of  each  question  to  the  part  of  the  inquiry 
with  which  it  is  concerned,  and  to  the  problem  as  a 
whole,  should  be  evident. 

Third. — The  schedule  form  itself  should  be  simple 
and  consistent  with  the  type  of  records  which  exist, 
so  that  supplying  the  information  desired  will  not 
involve  an  undue  amount  of  labor  and  occasion  error, 
because  of  the  necessity  for  reinterpreting  the  cus- 
tomary units  of  measurement. 

Fourth. — The  questions  should  be  simple,  and 
incapable  of  being  misunderstood;  and,  so  far  as  is 
possible,  answerable  by  ''yes"  or  "no,"  or  by  number. 
They  should  not  allow  of  evasive  answers,  and  should 
not  be  unduly  inquisitorial.  The  order  in  which 
they  are  asked  should  be  convenient  for  the  person 
addressed,  and  not  involve  unnecessary  duplication, 
or  arouse  a  suspicion  that  the  informant  is  to  be  in 
any  way  tricked  by  his  answer. 

Information  obtained  directly  from  business  records, 
or  from  schedules  based  on  records,  should  be  sub- 
jected to  a  thorough  editing  before  the  tabulation 
process  begins.  Evident  errors  due  to  omissions, 
additions,  false  interpretations,  or  misunderstandings, 
should  be  corrected  at  once.  Undue  tampering  with 
the  facts,  however,  is  to  be  guarded  against,  and  altera- 
tions made  only  in  case  of  unmistakable  error.  In 
all  cases,  alterations  should  be  made  evident  through 
the  use  of  some  distinctive  mark  or  ink  device.  It 
is  an  easy  matter  materially  to  change  the  nature  of 


CLASSIFYING  AND  TABULATING  THE  FACTS        53 

a  fact,  and  to  distort  the  truth  by  the  interchange  of 
a  few  items,  or  by  entrusting  the  editing  to  an  inex- 
perienced person.  So  far  as  possible,  the  returns 
should  be  made  consistent  with  the  facts,  and  complete. 
This  may  necessitate  the  return  of  the  schedule.  If 
it  does,  full  explanation  should  be  made  of  the  reasons 
for  returning  it,  and  cooperation  solicited. 

As  soon  as  data  are  properly  edited,  tabulation 
may  at  once  proceed.  This  should  be  begun,  how- 
ever, only  after  a  definite  plan  of  classification  has 
been  worked  out,  and  the  nature  of  the  problem  upon 
which  the  classification  is  to  throw  light,  clearly 
sensed.  All  of  the  considerations  noted  above  in  this 
respect  are  of  primary  significance.  Indeed,  in  many 
instances  the  nature  of  the  tabulation  wanted  deter- 
mines the  type  of  the  data  which  is  collected.  The 
order  of  procedure  in  periodic  studies,  for  instance, 
where  comparisons  are  currently  made,  is  first  to 
decide  upon  the  tabulations  which  are  wanted,  and 
afterward  to  collect  the  data  in  such  a  way  that  the 
purpose  will  be  realized.  In  analyses  of  a  trial  charac- 
ter, when  the  nature  of  the  data  is  not  known,  the 
form  of  tabulation  must  be  largely  experimental.  The 
form  which  it  takes,  even  in  such  cases,  simply  serves 
to  put  in  tangible  form  a  scheme  of  classification 
already  made. 

The  actual  tabulating  process  may  be  done  either 
by  machine  or  hand  methods.  Where  the  problem  is 
simple,  and  the  data  relatively  few,  hand  tabulation 
will  suffice.  Where  the  problem  is  complex,  and  the 
data  numerous,  some  sort  of  machine  tabulation  must 
be  employed.  There  are  on  the  market  two  standard 
mechanical  tabulating  machines,  the  Hollerith  and  the 


54  STATISTICS  IN  BUSINESS 

Powers,  Either  of  them  may  be  used  to  advantage 
in  large  establishments  where  continuous  and  elabo- 
rate use  is  made  of  statistical  data.  The  process  by 
which  tabulation  by  machine  methods  is  carried  on  is 
comparatively  simple,  and  need  not  be  described  here. 
In  selecting  statistical  data  from  secondary  sources 
such  as  the  Reports  of  the  United  States  Census  on 
Manufactures  or  Occupations,  or  from  such  widely 
used  journals  as  Bradstreet's,  care  should  be  used  to 
see  that  the  facts  are  comparable.  Simply  to  take 
prepared  figures  from  different  but  complementary 
sources,  good  in  themselves,  and  to  fit  them  into 
tables,  in  order  to  substantiate  a  belief,  or  to  see  the 
implication  of  your  problems  from  a  new  angle,  with- 
out at  the  same  time  subjecting  them  to  rigid  tests 
of  accuracy,  content,  and  application,  is  to  confuse 
the  mechanics  of  tabulation,  with  logical  analysis. 
Tabular  outlines,  neatly  filled  with  figures  which  prove, 
and  with  percentages  which  seem  to  show  relations, 
suggest  so  much  care  in  preparation  that  they 
often  carry  a  conviction  which  is  unwarranted.  Their 
neatness  and  form  seem  to  guarantee  the  nature  of 
their  contents.  Tabulation  is  always  a  means,  and 
not  an  end,  in  statistical  studies.  The  business  con- 
cern which  consents  consciously,  or  unconsciously,  to 
allow  elaborate  tabulations  of  facts  currently  to  be 
made,  without  continually  subjecting  them  to  tests 
of  validity,  and  application  to  particular  problems 
and  issues,  is  not  only  wasting  money  but  also  violat- 
ing the  fundamental  consideration  which  should  con- 
trol every  business;  namely,  the  scientific  point  of 
view. 


CHAPTER  V 
PRESENTING  THE  FACTS— GRAPHICS 

Classified  facts  may  also  be  expressed  graphically. 
There  is  a  psychology  about  graphic  presentation 
which  is  significant  and  which  business  can  not  afford 
to  ignore.  Through  tabulation,  facts  are  only  im- 
perfectly visualized.  Relations  do  not  stand  out; 
they  remain  abstract.  It  is  difficult  to  compare  more 
or  less,  to  see  differences,  and  to  appraise  the  amounts. 
Graphically,  however,  relations  are  seen;  there  is  an 
appeal  to  the  eye,  as  well  as  to  the  intellect.  A  fact 
is  emphatic  in  proportion  to  the  number  of  avenues 
through  which  it  makes  its  appeal. 

But  graphic  presentation  alone  will  not  suffice. 
Through  classification  and  tabulation,  facts  are  re- 
duced to  logical  order;  through  graphic  forms  they 
are  illustrated  according  to  this  order.  Graphic  pre- 
sentation adds  to  the  meaning  of  facts  by  throwing 
it  into  relief.  It  does  not  replace  tabulation;  it  com- 
plements it. 

In  selecting  diagrams  or  other  graphic  forms  serv- 
iceability, simplicity  and  truthful  representation  of 
the  facts  should  be  the  aim.  There  is  always  a  best 
form  in  graphics  as  there  is  in  tabulation.  The  same 
requirements  as  to  order  of  arrangement  of  details, 
spacing,  size  of  the  figure,  and  methods  of  making 
the  relations  between  facts  emphatic,  apply  here  as 
they  do  in  tabulation.     The  physical  work  of  charting 

55 


56  STATISTICS  IN  BUSINESS 

may  be  assigned  to  the  relatively  inexperienced;  the 
choice  of  the  forms  to  use  must  be  made  by  one  who 
not  only  understands  precisely  what  is  to  be  shown, 
the  psychology  of  the  persons  to  whom  it  is  addressed, 
but  also  appreciates  the  peculiar  appeal  of  the  differ- 
ent illustrations  that  are  available. 

In  choosing  graphic  figures  certain  elementary  but 
at  the  same  time  fundamental  principles  should  be 
followed. 

First. —  Avoid  figures  which  must  be  read  in  two  or 
more  dimensions. 

Second. — Guard  against  confusing  the  apparent 
with  the  real.  In  this  connection,  lines  or  bars  are 
superior  to  surfaces  and  solids. 

Third. — Accompany  graphic  forms  with  the  con- 
crete data  which  they  represent. 

Fourth. — ^See  that  the  fact  and  the  form  of  its  pres- 
entation agree. 

Where  areas  are  involved,  choose  some  form  of 
statistical  map  as  a  means  of  illustration.  Maps 
show  both  position  and  magnitude.  Data  may  be 
spread  out  on  them  and  studied  in  relation  to  space. 
Strive  for  that  degree  of  accuracy  in  map  making 
which  your  problems  require,  and  remember  that 
maps,  like  all  types  of  diagrams,  are  serviceable, 
primarily,  in  the  power  of  suggestion,  rather  than  in 
their  truthful  portrayal  of  precise  facts.  (See  Figs. 
21,  22,  23  and  24.)  Suit  the  graphic  device  to  the 
problem  to  be  solved.  Use  the  same  discrimination 
here  that  you  use  in  the  preparation  of  the  data  for 
illustration;  choose  the  means  in  conformity  with  the 
ends. 

Some  forms  of  data  may  be  shown  to  advantage  in 


PRESENTING  THE  FACTS  57 

graphs  or  curves.  When  a  continuous  picture  is 
desired,  either  as  a  means  of  describing  a  variable  fact 
at  one  time,  or  a  constant  fact  over  a  period  of  time, 
a  graph  or  curve  has  distinct  advantages  over  a  column 
of  figures.  If,  for  instance,  wage-rates  or  earnings  are 
to  be  studied,  reduce  them  to  graphic  form.  Choose 
scales  which  will  throw  them  into  relief,  but  which  will 
neither  exaggerate  the  exceptionally  large,  nor  lose 
sight  of  the  exceptionally  small  units.  Study  the 
direction  and  shape  of  the  distribution  and  try  to  see 
the  facts  in  relation  to  each  other,  and  to  the  whole. 

Along  the  horizontal  scale,  plot  the  measurements, 
and  on  the  vertical  scale  list  the  frequency  with  which 
each  measurement  occurs.  Make  the  steps  on  both 
scales  equal  units  (see  Figs.  4  and  20).  Under  no 
circumstances  should  there  be  doubt  as  to  the  meaning 
of  the  units  or  the  spaces  by  which  they  are  repre- 
sented. Let  the  illustration  be  a  faithful  representa- 
tion of  the  fact.  Do  not  attempt  to  give  an  arbitrary 
direction  to  the  curve,  nor  smooth  it  unless  the  imper- 
fections of  the  data  suggest  it,  or  the  character  of  the 
samples  makes  it  necessary.  The  classification  which 
precedes  the  graphic  presentation  is  the  means  of 
analyzing  it;  the  graphic  figure  chosen  is  the  device 
for  illustrating  it. 

When  the  facts  which  are  studied  are  historical, 
i.e.,  extend  over  a  period  of  time,  an  historical  curve 
may  be  used  to  illustrate  them.  Scientific  method  in 
the  classification  must  remove  the  uncertainties  of 
such  an  analysis.  Periods  which  have  nothing  in 
common,  and  units  of  measurements  which  have 
changed  during  the  periods,  cannot  be  compared. 
An  historical  curve  will  rarely,  if  ever,  reveal  incon- 


58  STATISTICS  IN  BUSINESS 

sistencies.  All  that  can  be  expected  of  it,  is  faith- 
fully to  record  the  changes  from  time  to  time.  If 
these  are  fictitious,  the  curve  is  not  to  blame;  the 
error  is  in  subjecting  them  to  this  treatment.  The 
analysis  is  fundamental ;  the  curve  only  suggestive. 

Business  executives  cannot  afford  to  ignore  the 
merits  of  graphic  presentation,  but  they  must  not  be 
deluded  into  the  belief  that  it  carries  with  it  a  magic 
which  makes  it  unnecessary  to  look  behind  it.  Reason- 
ing from  graphic  figures  alone,  where  the  conditions  of 
the  measurements  which  they  represent  are  not  known, 
violates  every  canon  of  scientific  method.  The  super- 
ficial is  confused  with  the  fundamental. 

Business  problems  and  business  facts  must  be  taken 
apart  and  scrutinized.  Classification  is  the  first  step 
in  this  process,  and  graphic  presentation  the  means  by 
which  the  classification  is  expressed.  No  business  is 
too  small  to  profit  by  this  approach,  and  none  is  too 
large  to  ignore  its  possibilities.  The  requirements  of 
scientific  method  furnish  the  conditions  under  which 
analysis  is  applied. 

It  is  impossible  in  a  brief  statement  adequately  to 
discuss  the  technique  of  graphic  presentation.  For 
a  more  complete  discussion  reference  should  be  made 
to  the  author's  '^ Introduction  to  Statistical  Methods," 
and  to  Brinton,  W.  C,  Graphic  Methods  for  Pre- 
senting Facts.  It  may  be  helpful,  however,  partly  in 
emphasis  of  what  has  been  said,  and  partly  for  the 
sake  of  convenience,  to  summarize  in  the  form  of 
general  rules,  the  salient  points  to  be  remembered  in 
the  use  of  graphic  figures.^ 

**' Rules  for  Graphic  Presentation  of  Statistical  Data,"  by  Day, 
Reed  and  Secrist.  Weekly  Statistical  News,  Central  Division  of 
Planning  and  Statistics,  Washington,  D.  C,  No.  5,  Oct.  10,  1918. 


PRESENTING  THE  FACTS  59 

A.  General  Make-up  of  Diagrams 

1.  Data  to  Accompany  Diagrams. — The  data  shown 
graphically  in  a  diagram  should  be  given  in  tabular 
form  either  beside  or  within  the  diagram,  or  in  close 
proximity  in  the  text.  Care  should  be  exercised, 
however,  to  place  figures  so  as  not  to  disturb  or  distort 
the  visual  impression  conveyed  by  the  chart.  (See 
Fig.  1  where  this  rule  is  followed,  and  Figs.  2 
and  3,  "where  it  is  violated.  In  Fig.  1,  for  instance, 
the  inclusion  of  the  concrete  data  makes  it  possible 
to  verify  the  percentages  upon  which  the  diagram 
is  drawn.     In  Fig.  2,  this  is  impossible.) 

2.  Scale  Units. — In  general,  in  the  laying  off  of 
scales,  the  scale  intervals  on  any  single  diagram  should 
be  exactly  proportionate  to  the  gradation  of  number, 
size,  or  time  represented  (the  logarithmic  scale  con- 
stitutes an  exception  to  this  rule).  (See  Fig.  4, 
where  this  rule  is  seriously  violated.  The  scale  units 
on  the  horizontal  axis  are  not  proportional  to  the  sizes 
of  the  groups  into  which  the  capital  data  are  divided. 
Had  the  rule  been  followed,  the  direction  of  the  curves 
would. have  been  distinctly  less  vertical  and  the  visual 
impression  different.  See  also  Fig.  20  where  the 
rule  is  violated  on  the  horizontal  axis.  If  the  space 
units  were  proportional  to  the  amounts,  the  curves 
would  be  drawn  out  much  farther  to  the  right.) 

3.  Scale  Figures. — Figures  for  the  scales  of  diagrams 
should  be  placed  at  the  left  and  at  the  bottom,  or 
along  the  respective  axes. 

4.  Base  Lines. — It  is  well  to  distinguish — as  by 
heavier  inking — lines  which  represent  standards  of 
attainment  or  bases  of  measurement  or  comparison. 


60  STATISTICS  IN  BUSINESS 

(See  Figs.  5  and  6.  In  the  first,  the  rule  is  violated; 
in  the  second,  it  is  followed.  In  Fig.  6,  the  base 
line  for  both  series  is  presumably  100,  and  constitutes 
— although  this  is  not  stated  on  the  diagram — the 
average  for  the  year,  the  monthly  prices  being  com- 
puted and  plotted  as  differences,  more  or  less  from  this 
amount.  In  Fig.  5,  both  prices  and  quantities 
are  measured  from  zero,  and  the  line  represent- 
ing it  should  have  been  inked  heavier  than  the  other 
lines.) 

5.  Arrangement  of  Items. — Items  should  be  grouped 
so  as  to  facilitate  the  comparison  of  those  most  sig- 
nificantly related.  Within  groups,  some  systematic 
order  should  be  adopted.  The  most  serviceable 
arrangements  are  according  to  (a)  the  sequence  of 
the  items  in  time,  with  the  earliest  at  the  left;  (6)  the 
size  of  the  items,  with  the  largest  at  the  top  or  at  the 
left;  or  (c)  the  favorableness  of  the  items,  with  the 
most  favorable  at  the  top  or  at  the  left.  (See  Figs. 
7,  8,  and  9.  In  Fig.  7,  the  amount  controls  the 
order  of  the  states,  the  largest  amount  coming  first. 
In  Fig.  8,  the  order  of  the  states  is  determined  by 
the  geographical  position  which  they  have  in  passage 
across  the  country  from  East  to  West.  In  Fig.  9, 
the  order  from  top  to  bottom  seems  to  be  haphazard. 
Frequency  would  have  suggested  itself  as  the  natural 
order.) 

6.  Position  of  Titles. — So  far  as  practical,  all  print- 
ing upon  a  diagram  should  be  placed  so  as  to  be 
read  with  ease  from  the  bottom  of  the  sheet.  (This 
is  pretty  much  a  matter  of  preference.  In  the  origi- 
nals of  the  following  figures  the  practice  was  about 


PRESENTING  THE  FACTS  61 

equally  divided.  So  far  as  the  writer  is  concerned, 
the  position  of  the  title  is  not  a  relatively  important 
matter.) 

7.  Use  of  Colors. — Where  a  need  for  duplicates 
may  arise,  charts  should  be  made  entirely  in  black 
and  white.  The  use  of  colors  is  not  recommended 
except  for  large  wall  charts. 

8.  Size  of  Sheet. — Avoid  irregular  sizes  of  paper. 
As  far  as  practical,  the  established  correspondence 
sizes  (8  X  lOyz  or  8>i  X  11)  should  be  used. 


B.  Choice  of  Graphic  Forms 

1.  For  Simple  Comparisons  of  Size. — (See  Figs. 
10  and  11,  where  surfaces  and  bars  are  used  as  alterna- 
tives for  illustrating  size.  In  all  of  the  figures,  bars 
or  single  dimension  illustrations  are  clearly  preferable. 
Avoid  such  an  illustration  as  Fig.  12.  In  Fig.  13, 
the  illustrations  are  suggestive  but  confusing  since 
the  scale  is  not  given  and  tw^o  dimensions  are 
used.) 

(a)  Bars. — Bars  are  the  most  satisfactory  graphic 
device  for  this  purpose.  In  general,  all  the  bars  used 
in  the  diagram  of  a  single  study  should  be  of  uniform 
width. 

(6)  Lines. — When  a  large  number  of  separate  items 
have  to  be  shown  in  a  single  diagram,  lines  may  be 
employed  in  place  of  bars. 

(c)  Position. — Bars  (or  lines)  are  best  placed  hori- 
zontally. 

2.  For  Comparisons  of  Component  Parts. — (See 
Figs.    14,    15,    and    16.     In   Fig.    14,    cross-hatched 


62  STATISTICS  IN  BUSINESS 

columns  are  placed  vertically,  and  in  Figs.  15  and 
16,  horizontally.  The  vertical  columns  are  more 
readily  compared  than  are  those  which  are  horizontal. 
In  Fig.  15,  the  more  recent  year  is  placed  at  the 
bottom,  while  in  Fig.  16,  the  order  of  the  years  is 
reversed.  These  figures  should  be  contrasted  with 
the  pie-diagrams  shown  in  Figs.  1,  2,  and  3,  as 
means  of  illustrating  component  parts.) 

(a)  Subdivided  Bars. — Subdivided  bars  are  the 
most  satisfactory  form  for  this  case. 

(6)  Cross-hatching. — Cross-hatching  is  the  best  way 
in  which  to  distinguish  component  parts. 

(c)  Position. — Horizontal  bars  are  to  be  preferred 
to  vertical,  except  when  the  items  are  separated  by 
intervals  of  time,  in  which  case  vertical  bars  should 
be  used. 

3.  For  Displaying  Frequency  Distributions. 

(a)  Vertical  Column. — ^In  general,  the  vertical  bar 
(or  column)  form  is  to  be  used.  The  straight-line 
histogram,  however,  is  a  satisfactory  alternative. 
(See  Fig.  20,  where  the  histogram  is  used.) 

(6)  Position  of  Scales. — The  scale  for  the  variable 
is  to  be  placed  along  the  horizontal  axis;  the  scale  for 
the  frequencies  along  the  vertical  axis. 

4.  For  Showing  Geographic  Variations. 

(a)  Dot  Maps. — Where  the  variable  takes  the  form 
of  varying  numbers  of  a  given  item,  the  situation  is 
best  represented  by  a  dot  map,  in  which  each  dot 
represents  a  fixed  number  of  cases.  All  of  the  dots 
should  be  of  uniform  size.  (Figs.  21,  22,  23,  and 
24,  show  four  types  of  dot  maps.  Fig.  21  gives 
only  an  impressionistic  view  of  frequency,  but  is  well 


PRESENTING  THE  FACTS  63 

fitted  for  this  purpose.  Places  of  ''high"  and  *'low" 
density  are  brought  out  in  a  remarkable  manner. 
Fig.  22  fails  of  its  purpose,  because  the  size  of  the 
dots  cannot  be  readily  compared.  The  exact  amount 
could  be  better  illustrated  by  a  cross-hatched  surface 
as  in  Fig.  24.  Fig.  23,  likewise,  illustrates  an  unsatis- 
factory map  device  for  much  the  same  reasons  as 
those  noted  concerning  Fig.  22.) 

(b)  Shaded  Maps. — Where  a  continuous  variable 
is  to  be  shown,  solid  black  and  white,  and  graded 
cross-hatched  areas  constitute  the  most  satisfactory 
form.  Care  should  be  exercised  to  secure  gradations 
of  intensity  of  black  and  white  corresponding  closely 
to  the  gradations  of  the  variable. 

6.  For  Showing  Time  Variations. 

(a)  Straight-line  Graph. — In  general,  the  use  of  the 
straight-line  graph  between  plotted  points,  is  to 
be  recommended.  (Fig.  25  shows  typical  straight- 
line  historical  graphs.  In  this  case,  two  vertical 
scales  are  employed,  and  care  must  be  used  in  inter- 
preting the  lines.  In  Figs.  18  and  26,  vertical  bars, 
and  in  Fig.  19,  horizontal  bars,  rather  than  con- 
nected lines,  are  used  to  show  data  historically. 
Where  the  increase  or  decrease  over  a  period  is  con- 
tinuous and  uninterrupted,  this  form  of  illustration  is 
satisfactory.  Where  the  tendency  is  irregular,  con- 
tinuous lines  should  be  used.  Care,  however,  should 
be  employed,  so  as  not  to  assign  meaning  to  the  direc- 
tion of  the  lines  connecting  the  points  when  they  are  un- 
related, and  to  confuse  absolute  with  relative  changes. 
In  this  connection,  see  Fig.  27  and  the  discussion 
relating  to  it.) 


64  STATISTICS  IN  BUSINESS 

(h)  Position  of  Scales. — Intervals  of  time  should  be 
scaled  invariably  along  the  horizontal  axis.  (See 
Figs.  13  and  19,  where  this  rule  is  violated.) 

(c)  Zero  of  Vertical  Scale. — There  is  a  strong  pre- 
sumption in  favor  of  the  appearance  of  the  zero  on  the 
vertical  scale  on  the  chart.  (On  the  logarithmic  or 
''ratio"  chart  there  is  no  zero  line.) 

(d)  Logarithmic  Scale. — The  vertical  logarithmic 
scale  is  to  be  used  when  rates  of  change  or  propor- 
tionate increases  and  decreases  are  to  be  emphasized. 
When  the  logarithmic  scale  is  employed,  the  limits  of 
the  scale  should  be  at  some  power  of  ten.  (See 
Figs.  28  and  29,  and  the  discussion  accompanying 
them.) 


These  rules  are  general,  and  should,  so  far  as  is 
possible,  be  applied  to  all  graphic  forms.  Each  busi- 
ness, however,  must  meet  its  problems  in  the  light  of 
their  peculiarities,  and  adjust  the  graphic  illustra- 
tions to  the  most  appropriate  ends.  The  making  of 
diagrams  and  curves  is  never  an  end.  Diagrams 
should  be  considered  as  a  means  of  throwing  light  on 
current  and  basic  problems,  and  should  constantly  be 
adjusted  to  the  individual  for  whom  they  are  prepared, 
and  the  problems  which  they  illustrate.  A  diagram 
designed  to  furnish  an  executive  with  a  concise 
picture  of  an  operation,  or  a  series  of  operations,  will, 
of  course,  be  different  from  one  which  is  designed  for 
the  public  at  large.  Graphic  forms  are  significant 
primarily  because  of  what  they  suggest,  and  the  psy- 
chology and  intelligence  of  the  group  for  which  they 
are  prepared   should  constantly..  be_ kept  in  mind. 


PRESENTING  THE  FACTS 


65 


Graphic  presentation  is  an  art,  and  too  much  atten- 
tion cannot  be  given  to  it  on  the  part  of  the  modern 
executive  who  desires  to  apply  to  his  business  the 
scientific  point  of  view. 

Fig.  1. — Pie-diagram  showing  the  distribution  of  total  stock  of 
hams,  bacon  and  shoulders,  reported  August  31,  1917. 


'Vrbolesale  Dealers  2.8% 


Retail  Dealers  3.3% 

MIecellaDeoai 
3.9% 


Stock  Reported  (Pounds). 

Meat  packers 361,932,276 

Storage  warehouses 25,512,057 

Wholesale  dealers 11,940,169 

Retail  dealers 14,368,359 

Miscellaneous 16,654,367 

Total 430,407,228 


The  above  figure  and  those  following  illustrate  dif- 
ferent forms  of  graphic  presentation.  Some  of  them 
follow  and  some  violate  the  rules  given  above — with 
what  consequence,  the  reader  must  in  large  part 
determine  for  himself.     Some  of  the  more  outstanding 


66 


STATISTICS  IN  BUSINESS 


virtues  and  limitations  of  the  figures  are  given  in  the 
comments  which  accompany  them. 

In  Fig.  1,  the  surface  of  the  circle  constitutes 
100  per  cent,  or  the  entire  amount  of  stocks  reported, 
as  shown  in  the  table  below  the  figure.  An  alternative 
and  generally  more  satisfactory  way  of  showing  com- 
ponent parts  is  by  using  bars  the  lengths  of  which  are 

Fig.  2. — Pie-diagram  showing  the  percentage  distribution  of 
the  world's  mill  supply  of  cotton  contributed  by  each  country; 
1917. 


proportionate  to  the  amounts  (see  Figs.  14,  15, 
and  16.)  The  table  beneath  the  illustration  would 
have  been  more  complete  had  it  contained  the  per- 
centage figures  illustrated  in  the  diagram. 

Fig.  2  is  faulty  in  not  containing  the  concrete 
data  on  the  basis  of  which  the  percentages  are 
computed.    Moreover,  the  relations  between  the  per- 


PRESENTING  THE  FACTS 


67 


centages  are  not  as  clearly  illustrated  as  they  would 
have  been  had  bar-diagrams  been  used.  (See  Figs. 
14,  15,  and  16.) 

The  pie-diagrams  below  are  presumably  drawn  in 
proportion  to  the  amount  of  the  goods  produced,  but 
there  is  nothing  in  the  illustrations  to  show  this,  nor 

Fig.  3. — Pie-diagrams  showing  the  percentage  distribution  of  the 
production  of  boots  and  shoes,  and  of  textiles,  bj^  states. 


1  MASSACHUSETTS 

2  NEW  YORK 

3  MISSOURI 

4  NEW  HAMPSHIRE 

5  OHIO 

6  PENNSYLVANIA 

7  lUJNOIS 


COTTON  GOODS. 
INCLUDING  COTTON 
SMALL  WARES 


BOOTS 


8  MAINE 

9  WISCONSm 

10  NEW  JERSEY 

11  MINNESOTA 

12  VIRGINIA 

13  MiCmOAN 

14  ALL  OTHER  STATES 


WOOLEN  a  WORSTED 

GOODS,  INCLUDING 

FELT  GOODS  a 

>V00LHAr5 


I  MASSACHUStllS 

I   M/SSSACHUSETTS 

2  NORTH  CAROUNA       8    NEW  HAMPSHIRE 

2 

POflSrLWNlA 

7    miNE 

3  SO\m  CAROUNA      9    AUBAMA 

3 

RHODE   ISLAND 

8    NCV  HAUPSHiRE 

4   RHODE  ISLAND         10   MAINE 

4 

NEW  JERSEY 

9     OHIO 

6   eEORSlA                   II    NEW   1TOA 

5 

NEW  YORK 

n    VIRGINIA 

0   PDtNSYLVANIA        12   NEW  JfRSEY 

6 

OONfCCTXWT 

II    AaOThERSWrO 

T  CONNECTICUT         13  ALL  OTHER.  STAItS 

is  the  scale  given  in  which  the  measurements  are  made. 
Moreover,  the  concrete  data  are  missing — both  the 
amounts  and  the  relationships  have  to  be  taken  on 
faith.  The  use  of  bar-diagrams  would  have  been 
preferable  here,  as  in  Figs.  1  and  2. 

Fig.  4  is  reproduced  exactly  as  it  appears  in  the 


68 


STATISTICS  IN  BUSINESS 


original.  It  is  defective  in  several  respects.  The 
vertical  scale  contains  the  unit  9000  instead  of  900. 
The  horizontal  scale  is  divided  into  uniform  spaces, 
but  these  are  related  to  varying  amounts.     The  in- 

FiG.  4. — Curves  showing  the  relation  of  farm  capital  to  labor  in- 
come on  260  general  farms  in  Monmouth  County,  New  Jersey. 

Labor  Income 
$1300 

1200 
1100 
1000 

9000 

800 

700 

600 

500 

400 

300 

200 

100 
0 

£oM  100 
200 


/ 

^--^ 

/ 

J 

4\ 

/ 

^ 

■V 

y 

"^ 

/ 

f  ^} 

V 

/ 

°f 

// 

/ 

/ 

// 

/ 

'/ 

// 

/   / 

/ 

/ 

'' 

3000 

$5001 

$7001 

$10001 

$15001 

$20001 

$30001 

to 

to 

to 

to 

to 

to 

and 

5000 

7000 

10000 

15000 

20000 

30000 

over 

Total  Capital  Invested  per  Farm 


terval,  presumably,  is  $2000  between  $3000  and  $7000 
(but,  see  the  different  ways  of  recording  the  lower  sides 
of  the  first  two  groups).  The  intervals  above  $7000 
are  in  order,  $3000,  $5000,  $5000,  $10,000,  and  an 
indefinite  amount,  but  the  scale  is  drawn  as  though 


PRESENTING  THE  FACTS 


69 


they  were  identical.     The  result  of  this  error  is  to 
give  a  false  direction  to  the  curves. 

The  base  or  zero  line  in  Fig.  5,  should  have  been 
more  heavily  inked  than  the  other  lines.  The  spaces 
assigned  to  the  months  represent  in  fact  a  series  of 
rectangles  the  heights  of  which  are  indicated  by  the 
positions  of  the  curves  at  the  middle  points.  The 
lines  connecting  the  points  on  the  production  curve 

Fig.  5. — Graphs  showing  the  price  and  production  of  eggs  by 
months  on  selected  farms,  Washington  Co.,  Ohio,  1912-1916. 


2.000 

40 

S 
30  1 

d 

0 
20Q 

U 

0 

0 

10  h 

P4 

0 

A 

^c, 

f 

V 

N 

^N 

/ 

Egg  Production  -  D02 

ill 

N 

^°> 

J  ' 

\ 

/ 

\ 

v 

\ 

/ 

/ 

AN 

^'- 

V 

-^ 

/ 

^ 

\ 

V 

^ 

s. 

-^ 

^ 

Not 

Dec 

Jsn. 

Feb. 

Mar 

Apr 

1 

M»y 

June 

July 

Aog 

Sep 

Oct. 

have  no  other  purpose  than  to  aid  the  eye  in  interpret- 
ing the  increase  or  decrease  from  month  to  month, 
and  in  noting  the  general  contour  of  the  curve.  The 
points  on  the  price  curve  for  the  months  presumably 
represent  averages  so  that  no  significance  should  be 
attached  to  the  lines  connecting  these  points.  It  is 
not  clear  from  the  curves  why  the  beginning  and  stop- 
ping points  are  not  the  middle  of  the  month  spaces. 
The  curves  clearly  show  the  inverse  relationship  be- 
tween production  and  price. 

The  base  or  100  per  cent,  line  in  Fig.  6  is  rightly 


70 


STATISTICS  IN  BUSINESS 


more  heavily  inked  than  the  other  lines  so  that  supply 
and  price  in  excess  and  in  defect  of  it  are  clearly  shown. 

Fig.  6. — Curves  showing  by  months  the  relative  supply  and 
price  of  Wisconsin  butter,  1914. 


200 
190 
180 

SUPPLY  AND  PRICES  OF  WISCONSIN 

200 
190 
180 

BUTTER-  1914 
Supply  Index     ..q- o— o— o o 

Price  Index 

170 
160 
150 
140 
a  130 

41 

o 

^120 

170 
160 

i 

1 

150 

1 
1 
1 

1 

\ 

\ 
V 

140 

1 

1 
1 

1 

\ 
\ 

\ 
\ 

130  5 
u 

120,2 

1 

! 

\ 
\ 

> 

1 
1 
1 

\ 

» 

y 

110 1 

100 

90 

80 

70 

( 
60 

50 

no 

100 
90 
80 

\ 

1 

1 
1 

i 

^ 

/ 

k 

S 

1 
1 

1 

^ 

^ 

/ 

\ 

/ 
/ 

r' 

t 
\ 

/ 
1 

1 

( 

/ 

70 
60 

50 

Jan.  Feb.  Mar.  Apr.  May  June  July  Aug. Sept.  Oct.  Nov.  Dec. 


It  will  be  noticed  that  the  100  per  cent,  line  bisects  the 
areas  inclosed  within  both  curves — that  is,  the  excesses 


PRESENTING  THE  FACTS  71 

are  equal  to  the  deficiencies.  In  this  figure,  the  months 
or  horizontal  units  are  indicated  by  a  line  rather 
than  by  a  space  as  in  Fig.  5.  There  are  eleven 
spaces  in  this  figure;  in  Fig.  5,  there  are  twelve 
spaces  for  the  year.  There  is  no  question  in  this 
figure  about  the  points  at  which  these  curves  should 
begin  and  end  as  there  is  in  the  preceding  one. 

From  the  curves  it  may  be  deduced  that  the  supply 
and  the  price  are  relative,  rather  than  absolute  num- 
bers, but  the  value  of  the  illustration  would  have 
been  increased  had  this  fact  been  stated  in  some  such 
form  as  follows: 

Average  monthly  price  for  the  year  =  100  per  cent. 

Average  monthly  supply  for  the  year  =  100  per 
cent.  Moreover,  the  concrete  data  should  have  been 
included  in  the  chart.  The  figure  clearly  shows  that 
the  price  of  butter  is  much  more  stable  than  is  the 
supply. 

The  bar-diagram,  (Fig.  7),  illustrates  the  stocks  of 
sugar  held  by  retail  dealers  by  states  in  the  order  of 
amounts.  The  largest  is  put  first  and  is  therefore 
given  emphasis,  but  the  reverse  order  would  have  been 
equally  good.  An  alphabetical  arrangement  of  the 
states  would  have  been  meaningless  for  the  purpose  of 
the  illustration.  The  bars  are  placed  horizontally  and 
are  disconnected.  Because  of  the  regularity  of  the 
decline  from  the  greatest  to  the  smallest  amount, 
little  advantage  would  have  accrued  from  connecting 
the  ends  of  the  bars  by  straight  lines.  The  diagram 
suggests  the  relative  amounts  and  that  is  all  that  it  is 
intended  to  do.  The  concrete  data  are  made  a  part 
of  the  diagram,  and  there  is  no  occasion  in  studying 


72 


STATISTICS  IN  BUSINESS 


Fia.  7. — Bar-diagram  showing  stocks  of  sugar  reported  by  retail 
dealers,  by  states,  August  31,  1917. 


Milliexis  of  Pounds 
4  6 


PRESENTING  THE  FACTS 


73 


Fig.  8. — Bar-diagram  showing,  by  statCvS,  and  for  farm  mortgages 
the  percentage  of  business  on  which  commission  is  paid. 


lK$T«ll«tlrt   COHMISSIOH 


No  CoHmuwM. 


74  STATISTICS  IN  BUSINESS 

the  illustration  to  determine  the  exact  amounts  for 
the  individual  states. 

The  bar-diagram,  (Fig.  8),  illustrates  for  each  of  the 
states  the  percentage  distribution  of  commissions  on 
farm  mortgages.  The  order  of  the  states  is  geograph- 
ical and  the  illustration  not  convincing  because  of  this 
fact.     If  the  size  of  "Installment   commission,"  for 

Fig.  9. — ^Bar-diagram    showing    the   per    cent,    distribution    of 
reasons  for  workmen  leaving  their  positions. 

WHY  MEN  LEFT 
REASONS  FOR  LEAVING 
REASONS     PERCENT 

WOT  ENOUGH  MONEY  ^  '  _  f-.^J 

NEVER  STARTED     6  :   ^ 


W0RK1W6  CONDtnONS  go  W^M^. 
DISCHARGED       sT^ni 

LAID  OFF if} 

DISSATISHED  s'  1 

BETTER  OOB        12 


n 


■-  "nv"      w^'i":"^';'  ;^;;?iy;cS."S!.:5 


NEEDED  AT HOME     81 
LIVING COWPmONS  St     i 
FAILED  TO  REPORT    8 
PEftSOHAL  REASOHS  7 


instance,  had  been  made  the  controlling  factor,  the 
dominant  element  in  the  illustration,  as  indicated 
by  the  shades,  would  have  been  made  emphatic. 
There  is  always  a  best  order  to  follow,  and  it  should 
govern  in  the  make-up  of  a  diagram. 

This  figure  shows  relative  rather  than  absolute 
amounts,  and  should  have  been  accompanied  by  the 
concrete  data  on  which  the  percentages  are  computed. 


PRESENTING  THE  FACTS 


75 


The  bar-diagram,  (Fig.  9),  is  defective  in  the  follow- 
ing particulars:  (1)  It  is  not  provided  with  a  scale. 
(2)  The  order  in  which  the  reasons  are  given  is  with- 
out significance:  it  is  not  emphatic.    (3)  The  concrete 

Fig.  10. — Surfaces  and  bar-diagrams  showing  for  specified  years, 
the  amount  of  wheat  in  bushels  purchaseable  for  $100.00. 


A  HUNDRED  DOLLARS*  WORTH  OF  WHEAT 


1913 


1914 


1915 


1916 


data  upon  which  the  percentages  are  calculated  are 
not  given. 

In  Fig.  10  surfaces  and  bars  are  used  as  alter- 
native illustrations.  The  ''sacks"  vary  both  in 
length  and  width,  and  the  question  is  raised  immedi- 


76 


STATISTICS  IN  BUSINESS 


ately:  Are  they  drawn  to  scale?    They  are  not  so 
drawn.     The  amounts  and  the  illustrations  may  be 
contrasted  as  follows,  if  1913  is  taken  as  100. 
Amounts:  1913  =  100;  1914  =  83;  1915  =  81;  1916 
=  54. 


Fig.  11. — Surfaces  and  bar-diagrams  showing  the  relationship  be- 
tween the  areas  of  Russia  in  Europe  and  the  Russian  Empire. 


RUSSIA  IN  EUROPE     l;B67,737  sq.m. 
ROSSIAN  EMPIRE         8,647,657  9q.m. 


2,500  5,000  7,500 

Square  Miles   On'OOO  ) 


10.00C 


Illustrations:     1913  =  100;    1914  =  67;     1915  =  54; 
1916  =  30. 

If  the  ''sacks"  are  thought  of  as  solids,  then  the 
discrepancy  between  the  fact  and  the  illustration 
is  much  greater.  The  drawings  were  presumably 
made  with  the  length  only  in  mind,  but  they  are 
deceptive  because  both  the  length  and  the  width  vary. 
For  surfaces,  the  dimensions  vary  as  the  square  roots 


PRESENTING  THE  PACTS 


77 


of  the  areas;  and  for  solids,  as  the  cube  roots  of  the 
contents. 

The  amounts  are  accurately  and  better  illustrated 
by  the  bars.     There  is  nothing  deceptive  about  them ; 

Fig.  12. — Surfaces  showing  the  relationship  between  total  coal 
production  and  savings  in  coal  consumption  resulting  from  cur- 
tailing light. 


their  accuracy  is  at  once  confirmed  by  the  scale  accord- 
ing to  which  they  are  drawn. 

In  Fig.  11,  surfaces  and  bars  are  used  as  alter- 
native illustrations.  Contrast  the  effect.  Which 
method  seems  to  you  preferable  as  an  illustration? 

In  Fig.  12,  surfaces  or  areas  within  areas  are 
used.     Because,  in  such  figures,  the  dimensions  vary 


78 


STATISTICS  IN  BUSINESS 


as  the  square  roots  of  the  areas,  comparison  is  very 
difficult,  if  not  impossible  to  visualize.  Such  illustra- 
tions ought  not  to  be  used. 

Fig.  13. — Surfaces  and  bar-diagrams  showing  gross  tonnage 
of  vessels  registered  in  Canada  and  Great  Britain,  engaged  on 
the  Great  Lakes  and  connecting  waters  west  of  Montreal. 


1899-1900 


Fiscal  Tmc 

No.  ol 
VcBBeli 

Orott 

Tonoft^e 

189S-I900 
1905  IQM 

i»iMai4 

Ut 

165 

90,»34 
167,626 

aio.iTS 

1905-1906 


1913-1914 


1899-1900 


400 


Gross  Tons     (  in  000  ) 


In  Fig.  13,  surfaces  and  bars  are  used  as  alter- 
native illustrations.  The  areas  of  the  ships  are 
significant  while  the  lengths  of  the  bars  are  all  that 
need  to  be  considered.  Both  illustrations  are  drawn 
on   absolute  scales.     The  use  of  figures  of  ships   is 


PRESENTING  THE  FACTS 


79 


suggestive,  but  the  illustration  is  inconclusive  because 
of  the  absence  of  a  scale  and  the  use  of  two  dimensions. 
Notice  the  optical  illusions  in  Fig.  14 :  the  bars  seem 
to  be  constricted  at  the  black  areas.  The  scale  is  unfor- 
tunately placed  at  the  right  rather  than  at  the  left  of 

Fig.  14. — Cross-hatched  bars  showing  the  distribution   of  the 
gross  income  of  selected  farmers  in  Wisconsin. 


Value  Supplied  by  tbe 
Farm  Toward  Family's 
LiTlog  Expense  (Estimated) 

Farmer'i)  Labor  Income 
Unpaid  Family  Labor 


InCereBt  on  Investment 


Depreciation  ol  Equipment 

Taxes  and  Insurance 

Bepaira 

Misc. Current  Expenses 

Feeds  Purchased 

Hired  Labor 


the  figure.  If  faint  guide  lines  were  drawn  across 
the  surface  of  the  diagram,  it  would  be  easier  to  make 
comparisons  of  the  total  and  relative  amounts. 

Fig.  15  shows  the  percentage  relationship  between 
the  areas  but  does  not  give  the  concrete  data  upon 


80 


STATISTICS  IN  BUSINESS 


which  the  distribution  is  made.  The  cross-hatching 
is  distinctive.  The  bars,  however,  should  have  been 
placed  vertically. 

Fig.  16  is  distinctive  in  having  both  the  concrete 
data  and  the  percentage  relationships  component  parts 
of  the  diagram.  The  order  of  the  years  is  the  reverse 
of  that  followed  in  Figs.  14  and  15. 

Fig.  15. — Cross-hatched  bars  showing  the  distribution  of 
areas  on  selected  farms  in  Washington  County,  Ohio,  1912- 
1916. 


PER    CENT 
40 


1912 
1913 1 
1314  j 


^■^^^^ 


m^ms^ 


mmmm 


.'"■■■i^^^i 


S-YEAR 
AVERAG1 


1^1^^^^ 


CORN     Rg]  SMALL  GRAIN      t^  HAY 


MISCEL.   CROPS 


In  Fig.  17,  a  double  percentage  scale  is  used.  The 
shipments  for  each  month  of  the  year  are  shown 
by  the  height  of  a  rectangle.  The  rectangles  are 
distinct,  uniform  in  width,  and  broad  enough  to 
be  emphatic.  Undoubtedly,  the  most  evident  thing 
from  the  diagram  is  not  the  percentage  amounts  for 
the  months  individually,  but  the  general  distribution 
throughout  the  year.  It  would  have  been  helpful  in 
the  interpretation  of  the  diagram,  if  the  absolute 
amount  which  is  distributed  on  a  percentage  basis 
throughout  the  year  had  been  made  a  part  of  the  illus- 


PRESENTING  THE  FACTS 


81 


tration.  The  accuracy  of  the  distribution  by  months, 
if  not  the  exact  amount  shipped  during  the  year, 
could  then  have  been  proved. 

Fig.  16. — Cross-hatched  bars  showing  the  per  cent,  distribu- 
tion of  stocks  of  sugar  reported  for  August  31,  1917  and  August 
31,  1916  for  important  groups  of  firms. 


1917 


1916 


Per  Cent 
40  50  60  70  80  90 


100 


Sngar  and  Storage 

•Irmp  mills        warehouaea 
and  refiueiiet 


Stocks  Reported  (Pounds) 


Group 

1917 

1916 

Quantity 

Per  cent. 

Quantity 

Per  cent. 

Total 

1,039,279,301 

100.0 

1,430,660,470 

100.0 

Sugar  and  sirup  mills 

and  refineries 

480,767,457 

46.3 

660,301,064 

46.2 

Storage  warehouses. . . 

146,728,359 

14.1 

428,077,562 

29.9 

Wholesale  grocers 

207,398,679 

20.0 

166,961,829 

11.7 

Large  users  of  sugar . . . 

66,581,728 

6.4 

49,856,328 

3.5 

Retail  dealers 

90,429,732 

8.7 

96,855,176 

6.8 

Miscellaneous 

47,373,346 

4.6 

28,608,511 

2.0 

In  Fig.  18,  the  bars  are  placed  vertically  and  are 
spaced  on  the  horizontal  axis  in  proportion  to  the 
time.  The  figure  is  defective  in  not  having  a  com- 
mon scale. 

In  Fig.   19,   the  horizontal   rectangular  bars  are 


82  STATISTICS  IN  BUSINESS 

joined  together  thus  giving  a  connected,  step-like 
curve  covering  the  entire  period.  The  widths  of  the 
bars,  moreover  are  proportionate  to  the  periods  be- 
tween successive  censuses.  Contrast  this  illustration 
and  Fig.  18,  which  also  depicts  a  fact  historically. 
Which  do  you  prefer,  a  vertical  or  horizontal  position 
for  the  bars? 

Fig.  17. — Bars    showing   per    cent   distribution   by    months  of 
Cheddar  cheese  shipments  from  Wisconsin  to  Chicago,  in  1911. 


CHEDDAR  CHEESE  SHIPMENTS  FROM  WIS.TO  CHICAGO  ILU. 
1911 


I 


•  ■ 

n  n 


In  Fig.  20,  the  wage  groups  for  each  class  of  wage 
earners  are  represented  on  the  horizontal  axis  by 
vertical  lines,  uniformily  spaced  throughout  the  dia- 
grams. It  should  be  noted,  however,  that  the  rule 
which  requires  the  spaces  to  be  proportionate  to  the 
size  of  the  groups  is  violated  for  the  group  ''Under 
$3.00,"  and  for  all  groups  above  $16.00.  The  effect 
of  widening  the  spaces  so  as  to  make  them  propor- 
tionate to  the  size  of  the  groups  both  at  the  beginning 


PRESENTING  THE  FACTS 


83 


and  the  end  of  the  curves  would  be  to  give  them  a 
flatter  and  more  dispersed  appearance. 

The  concrete  data,  here,  as  in  so  many  diagrams, 
unfortunately  are  missing. 


Fig.  18. — Bar-diagram  showing  values  of  products  in  leading 
industries,  1879-1913.     (Values  in  millions  of  dollars.) 


328' 


,33& 


t85 


!68 


137 


S2 


SZ2 


BOOTS  &  SHOES 

EXCLUSIVE  OP  CUT  STOCK 
AND    FINDINGS 


THE  TEXTILE  INDUSTRIES 

COTTON  .  WOOLEN  ,  AND 
WORSTED  GOODS 


The  value  of  a  frequency  dot  map,  as  illustrated 
in  Fig.  21,  is  that  it  gives  a  clear  idea  of  density 
and  distribution,  and  change  from  "highs"  to  ''lows." 
It  is  easy  from  such  a  map  to  visualize  places  of  con- 


84 


STATISTICS  IN  BUSINESS 


centration  and  "  scatteration. "  The  value  of  each 
dot  is  of  little  consequence  in  reading  exact  frequency, 
since  the  chief  purpose  of  the  map  is  only  to  give 
an  impressionistic  view. 

Fig.  19. — Cross-hatched  bars  showing  by  census  years,  the  pro- 
portion of  urban  population  to  total  population  in  Massachusetts, 
1790-1910. 


The  type  of  map  illustrated  in  Fig.  22,  is  unsatis- 
factory because  the  sizes  of  the  dots  are  not  readily 
comparable.  If  it  is  not  desired  to  show  exact 
amounts,  then  the  scale  is  useless;  if  it  is  so  desired, 
the  illustration  fails  of  its  purpose. 


PRESENTING  THE  FACTS 


85 


Such  a  map  as  that  shown  in  Fig.  23,  is  unsatis- 
factory; neither  the  size  nor  the  shading  of  the  dots 
being  readily  comparable. 

Fig.  20. — ^Frequency  graphs  showing  the  percentage  wage  distri- 
bution of  classified  wage-earners  by  wage  groups. 


30r 


BOOTS  AND  SHOES 

EXCLUSIVE  OF  CUT  STOCK  AND  FINDINGS. 


<J^     "^      40      to 


OOI_l-»J^^    PER.    WEEK 


THE    TEXTILES 

COTTON. WOOLEN. AND  WORSTED  GOODS. 


—  1!^^ 


♦^ 


P01-L>^F8.S      PER.      WEEK ^^ 


In  Fig.  27,  the  ''bars  are  placed  vertically  .  .  .*  .  and 
the  so-called  'curve'  is  formed  by  introducing  the 
line  connecting  the  points  at  the  end  of  the  bars. 


86 


STATISTICS  IN  BUSINESS 


1 


PRESENTING  THE  FACTS 


87 


"Now  it  is  evident  that  the  only  things  properly  comparable  in 
such  a  chart  are  the  distances  from  the  base  line  to  the  points 
determined — in  other  words,  the  length  of  the  bars.  The  intro- 
duction of  the  distinctive  connecting  line  at  once  diverts  attention 
from  the  proper  comparison  to  the  line  itself.  If,  as  is  usually  the 
case,  the  bars  be  not  introduced  the  gradient  or  steepness  of  the 
line  becomes  then  inevitably  the  basis  of  judgment  and  all  notion 
of  the  distances  as  the  real  subject  of  comparison  is  lost.  Un- 
consciously the  line  is  erroneously  interpreted  as  expressing  rate 
of  change.     But  rate  of  change  ....  can  only  be  accurately  re- 

FiG.  22. — Varjdng-size  dot  map  showing  amounts  of   primary 
shipments  of  American  Cheese  from  Wisconsin,  1911. 


presented  by  a  ratio  chart  in  which  percentage  differences  and 
not  arithmetic  differences  are  plotted. 

"Moreover,  it  often  happens  that  a  large  part  of  the  scale  has 
no  points  assigned  to  it.  In  that  case  it  is  common  practice  to 
omit  the  lower  portion  of  the  scale.  This  at  once  and  completely 
renders  impossible  the  only  significant  comparison.  Suppose  the 
smallest  magnitude  in  a  given  group  be  75  and  a  larger  magnitude 
be  100.  It  would  then  be  in  accord  with  common  practice  to  cut 
away  the  lower  portion  of  the  scale  to,  say,  70.  The  ocular  com- 
parison of  the  two  magnitudes  will  now,  of  necessity,  be  that 


88 


STATISTICS  IN  BUSINESS 


between  5  and  30  and  not  between  75  and  100.  The  chart  then 
becomes  not  only  useless  but  positively  deceptive.  Furthermore, ' 
when  the  series  of  magnitudes  or  number  of  lines  becomes  increased 
beyond  two  it  becomes  difficult,  if  not  impossible,  to  compare  the 

Fig.  23. — Varying-shade  dot  map  showing  the  amount  of 
dairy  butter,  in  pounds,  produced,  sold,  and  consumed,  in  Wis- 
consin Counties,  1909. 


distances  even  though  the  entire  scale  be  given.  If  this  is  further 
complicated  by  an  abbreviated  scale  the  situation  becomes  one  of 
obscurity  multiplied  by  deception." 

Frequently,  it  is  desired  to  show  graphically  per- 


I 


PRESENTING  THE  FACTS 


89 


3 

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o 

00 
S3 


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90 


STATISTICS  IN  BUSINESS 


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1 

PRESENTING  THE  FACTS 


91 


Fig.  26. — Bar-diagram  showing  the  relative  growth  in  investment 
and  in  electricity  sold  in  kilowatt  hours,  for  years,  1896-1913. 


720.000,000 


$.40^,000.000  ~ 


1897  .18W  1901  1903  1905  1907  1909  1911  1918 
-  Years 


Fig.  27. — Combination  bar-diagram  and  line  chart. 


242    192 

199 

179    153 

ie7 

127 

101 

■\ 

225- 

\ 

HO- 

"■~«.  

— 

1 

TS- 

1 

1 

1907    1908 

1909 

1910   1911 

1912 

1913 

1914 

92  STATISTICS  IN  BUSINESS 

centage  rather  than  absolute  changes.  The  ordinary 
graphs,  such  as  those  above,  show  absolute  changes  or 
differences.  When  percentages  are  to  be  shown,  a 
''ratio,"  or  logarithmic  scale,  must  be  used.  Arith- 
metic or  difference  scales  and  percentage  or  ratio 
scales  are  illustrated  and  described  immediately  below 
in  an  article  prepared  by  Lucian  W.  Chaney. 

Arithmetic  Scale 


10 

1 

? 

20 
1 

30                            40 

1                               1 

'? 

60 

1 

f 

f 

20 

Percentage  Scale 
40                             80 
1                               1 

160 

1 

320 

1 

"It  will  be  noted  that  in  the  arithmetic  scale  equal  linear 
distances  represent  equal  arithmetic  differences,  whereas  in  the 
percentage  scale  equal  linear  distances  express  equal  percentage 
differences.  In  the  case  of  the  arithmetic  scale  one  space  repre- 
sents 10  units;  in  the  percentage  scale  one  space  represents  100 
per  cent,  difference. 

"If  it  is  desired  to  introduce  intermediate  numbers  in  the  above 
arithmetic  scale,  the  space  between  any  two  of  these  will  be 
divided  into  10  equal  parts.  Eleven  would  then  be  one  unit  from 
10,  while  15  would  be  midway  between  10  and  20,  since  points 
having  equal  arithmetic  differences  are  always  equidistant.  The 
construction  of  a  complete  percentage  scale,  on  the  other  hand,  is 
more  complicated  because  the  relation  of  any  magnitude  as  com- 
pared with  an  ascending  or  descending  series  of  magnitudes  is  a 
constantly  changing  percentage.  To  illustrate:  From  100  to 
110  is  a  10  per  cent,  increase,  whereas  from  200  to  210  the  increase 
is  only  5  per  cent.  Therefore,  on  a  percentage  scale  the  linear 
distance  from  200  to  210  will  be  less  than  that  from  100  to  110. 
Thus  it  is  seen  that  in  passing  up  the  percentage  scale  numbers 
separated  by  the  same  difference  as  regards  magnitude  will  be 
represented  as  drawing  closer  together  on  account  of  the  decreasing 
percentage  of  difference. 

"Suppose  it  is  desired  to  locate  the  intermediate  number  15 
on  the  percentage  scale  given  above.  In  order  to  do  this  the  fun- 
damental method  is  to  find  from  logarithmic  tables  the  logarithms 


PRESENTING  THE  FACTS 


93 


^      ft    d 


O        CO  *3  ^ 


03 
4) 

"3 


3 

a, 
o 


.a    :=; 


I 

o 


03 

Si 


s 


oeri 


o  0=  2 


94  STATISTICS  IN  BUSINESS 

of  10,  15,  and  20  and  then  place  15  in  a  position  representing  the 
relation  between  its  logarithm  and  those  of  10  and  20.  When  this 
is  done  it  will  be  found  that  15  is  not  equally  distant  from  10  and 
20  as  in  the  arithmetic  scale,  but  is  nearer  to  20,  as  shown.  This 
accords  with  the  fact  already  shown  by  illustration  that  the 
relation  of  a  given  value  to  an  increasing  series  is  a  constantly 
decreasing  percentage." 

It  is,  of  course,  unnecessary  to  prepare  your  own 
ratio  paper,  since  various  types  may  be  secured  in  the 
trade.  Figs.  28  and  29,  respectively,  taken  from 
Fisher,  ''The  'Ratio'  Chart,"  show  the  population  of 
the  United  States  plotted  on  a  ratio  and  on  a  differ- 
ence basis. 

Professor  Chaney  has  the  following  to  say  concern- 
ing the  characteristics  and  functions  of  the  "ratio" 
chart. 

"1.  In  a  ratio  chart  a  given  linear  distance  on  the  scale  always 
represents  the  same  percentage  difference. 

"2.  The  gradient  or  steepness  of  the  lines  always  and  inevitably 
expresses  the  exact  rate  of  change  in  any  series  of  statistical  facts. 
Consequently,  equal  rates  of  change  or  equal  percentages  of  differ- 
ence will  have  the  same  gradients.  If  two  magnitudes  vary  10 
per  cent,  upward  their  curves  will  run  parallel  however  far  sepa- 
rated they  may  be  on  the  chart.  For  example,  if  one  magnitude 
increases  from  10  to  11  while  another  increases  from  100  to  110 
the  curves  corresponding  to  the  change  will  be  parallel,  indicating 
the  same  rate  of  change.  It  is  evident  that  plotting  the  same 
magnitudes  on  an  arithmetic  scale  would  show  ten  times  the 
amount  of  difference  in  the  second  case  although  the  percentage 
difference  is  identical. 

"3.  The  percentage  scale  in  the  ratio  chart  has  no  zero. 
A  moment's  consideration  will  show  that  this  must  necessarily  be 
true.  As  long  as  there  are  magnitudes  to  be  plotted,  no  matter 
how  small,  the  percentage  decrease  can  never  be  100  and  thus 
can  never  theoretically  reach  the  zero  point.  .  .  .  The  absence 
of  the  zero  in  the  ratio  chart  is  sometimes  misapprehended  as  a 


PRESENTING  THE  FACTS 


95 


disadvantage.     On  the  contrary,  the  particular  value  of  the  scale 
is  related  to  this  fact.     Because  of  the  absence  of  the  zero,  atten- 


o 

1—1 


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tion  is  necessarily  and  properiy  centered  upon  the  relations  of  the 
various  magnitudes  to  each  other  and  particulariy  upon  the  rates 
of  change. 


96  STATISTICS  IN  BUSINESS 

"4.  The  ratio  chart  makes  possible  a  direct  and  correct  com- 
parison of  increases  and  declines.  The  usual  method  of  expressing 
changes  up  or  down  is  to  say,  for  example,  that  a  rise  of  50  per 
cent,  was  followed  by  a  decline  of  30  per  cent.  This  mode  of 
expression  is  used  without  realization  that  it  involves  expressions 
which  cannot  be  compared  one  with  the  other.  Comparatively 
few  persons  at  once  recognize  that  an  increase  of  100  percent,  is 
exactly  balanced  by  a  decline  of  50  per  cent.  Percentages  of 
increase  can  be  properly  compared  with  other  percentages  of  the 
same  sort  and  percentages  of  decline  are  similarly  comparable, 
but  no  direct  comparison  can  be  made  between  a  percentage  of 
increase  and  a  percentage  of  dechne." 


J 


CHAPTER  VI 

SUMMARIZING  THE  FACTS— AVERAGES  AND 
OTHER  MEANS 

The  viewpoint  of  the  business  man  who  is  willing 
to  act  on  the  basis  of  facts  is,  What  does  the  analysis 
show?  To  what  conclusions  does  it  lead?  The 
demand  is  for  some  form  of  a  summarized  statement. 
The  details  must  be  shortened,  or  crowded  together 
into  a  single  expression.  Not  that  they  are  of  no 
significance,  but  as  details  they  are  impossible  of 
being  readily  handled.  A  total  which  summarizes 
the  different  parts,  or  an  average  which  seems  to 
characterize  the  detail,  and  which  can  be  compared 
with  similar  figures  over  a  period,  or  for  different 
conditions,  is  what  is  wanted. 

Men  of  action  are  sometimes  impatient  with  details 
and  treat  them  as  though  they  were  identical  and 
uniform,  and  could  be  ignored.  They  are  inclined  to 
look  upon  them  as  "details,"  which  will  take  care  of 
themselves.  This  attitude  is  suggestive  of  the  state 
of  mind  which  looks  upon  business  as  simple,  and  its 
processes  as  capable  of  being  reduced  to  a  few  under- 
lying principles,  which  can  better  be  felt  than  stated; 
better  expressed  as  axioms  than  as  relative  truths. 
The  point  of  view  is  what  may  be  termed  absolute 
rather  than  relative.  It  looks  with  suspicion  upon 
diagnosis,  and  is  rather  content  with  generalization. 
It  tends  to  ignore  the  fundamental  truth  that  busi- 

7  97 


98  STATISTICS  IN  BUSINESS 

ness  is  diverse  and  the  situations  with  which  it  deals 
ever  changing,  and  to  accept  the  dogma  of  status. 
It  is  impatient,  for  instance,  with  the  idea  that  labor 
is  more  than  a  commodity,  that  the  market  cannot  be 
stated  in  single  terms  of  "demand  and  supply," 
and  that  a  protective  tariff,  competition,  or  free  trade 
have  limitations  depending  upon  the  type  of  national 
industry,  necessity  for  state  control,  and  the  interests 
of  classes. 

Now,  this  type  of  mind  has  both  its  strength  and 
limitations.  There  are  a  comparatively  few  funda- 
mental underlying  business  truths  resting  on  human 
psychology,  the  extent  of  industrial  development, 
etc.,  but  they  are  relative  for  time  and  place,  and 
are  not  absolute.  They  are  discovered  not  by  intui- 
tion, but  by  analysis.  Neither  can  they  be  divorced 
entirely  from  the  detail  of  business  operation,  trade 
relation,  and  human  conduct.  Average  market 
conditions  may  be  accurately  stated.  Likewise  the 
response  of  the  average  individual  to  a  type  of  adver- 
tising, for  instance,  may  be  calculated.  Business, 
while  it  can  not  overlook  these  underlying  truths,  can- 
not always  be  sure  that  a  particular  unit  will  benefit 
or  suffer  from  them.  All  of  the  conditions  which  give 
rise  to  them  may  not  be  experienced  in  every  busi- 
ness. There  are  some  which  are  above  and  some  which 
are  below  the  norm  established  for  business  as  a 
whole.  For  instance,  it  may  be  true  that  costs  vary 
with  industrial  output,  but  the  rate  is  different  for 
different  producing  establishments.  The  business 
which  is  built  on  a  general  cost  basis,  will  have  diffi- 
culty, under  certain  conditions,  in  financing  its  opera- 


SUMMARIZING  THE  FACTS  99 

tions;  and,  under  other  conditions,  will  be  realizing 
enormous  profits. 

The  point  which  it  is  desired  to  emphasize  is  that 
there  are  variations,  among  individual  businesses, 
from  the  norm  established  by  business  as  a  whole,  and 
these  should  not  be  lost  sight  of  in  the  daily  conditions 
of  operation.  A  business  unit,  large  or  small,  must 
shape  its  policy  on  its  past  experience  and  on  the 
experience  of  business  as  a  whole,  but  it  cannot  be 
blind  to  the  fact  that  most,  if  not  all,  of  these  are 
relative  only,  and  that  new  conditions  and  new  prob- 
lems are  always  suggesting  and  making  necessary 
changes  and  readjustments. 

What  has  been  said  has  particular  application  to  the 
subject  of  this  chapter.  Averages,  in  the  terms  of 
which  business  is  wont  to  express  its  condition  and  to 
compare  its  operations,  should  not  be  regarded  as  ''a 
secret  something  which  determines  events  ..." 
After  calculating  a  certain  average,  business  is  likely 
to  conclude  that  some  secret  fate  is  at  work  and  to 
expect  a  faithful  and  continuous  repetition  of  this 
average.  Every  average  is  a  sort  of  fictitious  substi- 
tute for  the  details  which  it  replaces,  serviceable  when 
the  conditions  for  which  it  stands  are  known,  but 
deceptive  when  they  are  ignored. 

The  truth  of  this  contention  should  be  seen  more 
concretely.  Business  profits  may  be  stated  as  aver- 
ages. In  this  form  they  are  convenient.  A  statement 
of  the  average  wage  which  is  paid  to  a  diverse  labor 
force  may  carry  some  meaning  to  the  business  execu- 
tive. Likewise,  costs  over  a  period  of  time  may  be 
averaged  in  order  to  detect  improvement,  or  the  reverse. 
But   profits   are   different    on    different   goods.     On 


100  STATISTICS  IN  BUSINESS 

one  the  mark-up  is  20  per  cent.;  on  another  50  per 
cent.  On  one  the  turn-over  per  year  is  ten;  on  the 
other,  two.  Can  these  differences  be  ignored  in  the 
single  expression  ^'average  profits?"  Likewise,  the 
average  wage  paid  may,  for  comparative  purposes,  be 
a  satisfactory  way  of  stating  the  wage  bill;  but  is  it 
significant  in  meeting  the  demands,  on  the  part  of 
labor  representatives,  for  increased  wages,  or  satis- 
factory to  the  employer  in  contrasting  amounts  paid 
and  services  secured?  Similarly,  average  costs  are 
deceptive  unless  the  conditions  of  their  measurement 
are  identical. 

The  burden  of  what  has  just  been  said  is  that 
general  impressions,  whether  expressed  as  averages  or 
otherwise,  will  not  suffice  in  business.  Averages  con- 
stitute norms  with  which  experience  may  be  compared, 
but  comparison  is  valid  only  when  conditions  are 
identical.  It  is  a  legitimate  endeavor  of  business  to 
set  up  for  different  types  of  enterprises  norms  or 
average  conditions  which  will  serve  as  guides  in  test- 
ing operations.  However,  these  standards  must  be 
precise,  and  the  conditions  to  which  they  apply, 
uniform.  For  many  purposes,  the  differences  from 
the  average  are  far  more  significant  than  the  norm 
itself,  since  they  measure  the  relative  degree  with 
which  it  is  experienced. 

Let  us  apply  what  has  been  said  to  the  different 
types  of  averages  which  should  be  used  in  the  analysis 
of  business  problems. 

First,  there  is  the  generally  known  arithmetic 
mean,  or  average.  It  is  on  the  tongue  of  every  busi- 
ness man,  and  is  probably  the  most  generally  used 
summary   expression.     What   does  it  mean?    It   is 


SUMMARIZING  THE  FACTS  101 

that  amount  which  results  from  dividing  the  sum  of  a 
series  of  numbers  by  the  number  in  the  series.  Spe- 
cifically, the  average  sale  from  the  following  experi- 
ence—Sl.OO,  $5.00,  $3.28,  $.60,  $2.22,  $4.81,  $.10— is 
$2.43.  What  is  this  average?  Plainly,  it  is  the  center 
of  gravity,  or  balancing  point  in  the  series,  the  numbers 
larger  than  it  being  exactly  balanced  by  those  smaller 
than  it.  It  is  clearly  not  represented  in  the  series 
at  all.  In  this  sense,  it  is  purely  fictitious.  It  is 
unreal.  In  another  series,  however,  this  average  may 
be  represented  in  every  number,  as  in  the  series  $2.43, 
$2.43,  $2.43,  $2.43;  average  $2.43.  In  still  another, 
it  may  be  closely  approached  by  some  of  the  items 
and  widely  separated  from  others,  as  in  the  series, 
$2.39,  $2.41,  $2.45,  $2.46,  $.10,  $.15,  $9.62,  $.26, 
$2.03;  average  $2.43. 

What  are  its  characteristics?  First,  all  of  the  items 
have  to  be  included  in  the  computation.  Second,  all 
of  the  items,  though  different,  are  treated  as  identical 
in  the  divisor.  Third,  it  is  not  of  necessity,  though 
it  may  be,  represented  in  a  series.  Fourth,  in  giving 
the  result,  each  item  is  significant  according  to  its 
size. 

The  average  (arithmetic  mean)  as  such,  tells  one 
nothing  concerning  the  series  out  of  which  it  is  made. 
The  differences  from  it  may  be  large  or  small;  how 
large  or  how  small  is  not  known.  It  ignores  the 
detail.  It  groups  different  conditions  together,  and 
reduces  them  to  a  hypothetical  common  denominator 
by  an  arbitrary  process  of  division. 

Are  business  operations,  or  experience,  or  groups 
of  them,  capable  for  practical  purposes  of  being  so 
described?     What  is  needed  is  not  a  purely  hypo- 


102  STATISTICS  IN  BUSINESS 

thetical  center  of  gravity,  which  the  average  gives,  but 
a  description  of  the  differences  from  the  average,  and 
the  manner  in  which  they  are  distributed  about  it. 
Take,  for  example,  wages  or  transportation  costs. 
What  is  needed  adequately  to  express  either,  so  as  to 
set  them  in  their  true  light  for  business  planning  and 
the  solution  of  the  problems  to  which  they  give  rise, 
is  some  measure  of  their  distribution  for  the  same  or 
for  different  classes.  What  are  the  extremes;  what 
is  the  most  common  wage  or  cost;  above  or  below 
what  figure  do  the  bulk  of  the  instances  fall? 
What  is  the  average  difference  from  the  average,  and 
to  what  are  the  wide  differences  due? 

When  doubt  arises  as  to  details,  appeal  is  made  to 
averages.  They  have  been  called  the  business  man's 
excuse  for  laziness.  They  might  also  be  called  the 
device  par  excellence,  for  dealing  in  glittering  generali- 
ties. As  averages  are  often  used,  both  indictments 
are,  without  doubt,  largely  true.  The  scientific  point 
of  view  does  not  require  that  averages  be  repudiated, 
but  it  does  provide  that  they  shall  be  used  with  in- 
telligence and  discrimination. 

However,  there  are  many  significant  uses  of  the 
average  (arithmetic  mean).  Statistics  has  been  called 
by  some  the  ''science  of  averages,"  and  appeal  is 
often  made  to  the  "law  of  averages."  What  is  this 
law?  Business  and  other  experiences  tell  us  that  it 
is  unnecessary  in  many  problems  to  measure  all  of  a 
series  or  to  count  all  of  the  instances  with  which  we 
deal.  Not  all  butter  is  sampled  when  purchased, 
nor  all  cotton  scrutinized  when  graded.  In  an  analy- 
sis of  markets,  appeal  may  be  made  to  the  law  of 
averages.     In  keeping  with  the  general  principle  that 


( 


SUMMARIZING  THE  FACTS  103 

the  average  height  of  a  number  of  people  may  be 
secured  by  studying  the  heights  of  a  few  thousand 
drawn  at  random  from  a  larger  body,  the  response  to 
a  selling  or  advertising  campaign,  for  instance,  may 
be  established  from  an  analysis  of  a  well  selected 
group  of  samples.  It  is  unnecessary  to  include  every- 
body, but  it  is  essential  that  each  characteristic  of 
the  group  shall  be  represented  in  the  samples  taken. 
Realizing  this  fact,  business  enterprises  are  appealing 
to  the  law  of  averages  in  studying  markets  and  in 
testing  advertising  media.  How  truly  samples  may 
be  representative,  however,  is  often  times  difficult  to 
establish.  Scientific  observation  may  be  difficult. 
The  peculiarities  of  a  group  may  not  be  revealed 
from  the  samples  taken,  and  serious  error  result 
from  generalizing  broadly  from  samples  which  can  be 
measured. 

The  value  of  sampling  as  a  method  is  conditioned 
by  the  degree  to  which  a  part  represents  a  whole. 
Too  frequently  samples  are  employed  with  the  belief 
that  ''other  things  will  remain  equal."  In  measuring 
physical  phenomena,  the  most  accurate  result  may 
be  secured  by  averaging  all  measurements,  if  there  is 
no  bias  in  the  unit  of  measurement,  if  allowance  is 
made  for  the  personal  equation,  and  if  measurements 
are  made  under  similar  conditions.  Business  phenom- 
ena, however,  are  constantly  changing.  Samples 
which  will  suffice  in  one  period  will  be  inadequate  at 
another.  Conditions  of  time,  place  and  income,  as 
well  as  the  psychology  of  the  groups  to  which  the  meas- 
urements apply,  are  constantly  in  a  state  of  flux,  and 
one  should  not  place  too  much  reliance  in  the  compen- 
sation  of  errors.     Business  conditions   change   with 


104  STATISTICS  IN  BUSINESS 

the  temper  of  the  people,  with  political  practices  and 
principles,  with  labor  unrest,  etc.  Blindly,  to  take 
an  average  in  the  hope  that  the  law  of  compensating 
errors  will  always  give  a  perfect  picture  from  imperfect 
detail  is  economically  suicidal. 

The  peculiarities  of  the  arithmetic  mean,  as  an 
average,  cannot  be  removed.  All  of  the  items  which 
enter  into  it  are  given  equal  weight;  they  are  all 
treated  the  same  in  the  divisor,  and  the  product  of 
the  division  is  almost  invariably  hypothetical.  As  a 
single  summary  figure,  it  is  often  unsatisfactory.  In 
I  /  time  comparisons,  it  is  generally  misleading  if  the 
data  out  of  which  it  grows  are  not  homogeneous. 
The  same  is  equally  true  when  it  is  applied  to  geo- 
graphical or  frequency  data.  An  average  of  this  type 
may  not  only  be  unrepresentative  but  deceptive. 
The  average  daily  output  of  a  factory  over  a  period 
may  remain  constant  and  yet  the  production  in 
various  departments  change  radically.  Similarly, 
the  average  wage  paid  may  remain  constant  and  the 
wage  scale  seriously  slump  or  rise  at  the  lower,  middle 
or  upper  groups. 

But  there  are,  of  course,  other  averages.  These, 
however,  are  less  commonly  used,  although  for  many 
purposes  they  are  superior  to  the  arithmetic  mean. 
They  are  averages,  however,  and  are  subject  to  many 
of  the  limitations  which  are  characteristic  of  the 
arithmetic  mean. 

Probably  the  most  familiar  of  the  other  ways  of 
characterizing  complex  details,  is  to  use  the  median. 
The  median  is  the  middle  item  in  a  series  arranged 
in  the  order  of  size,  and  divides  the  group,  therefore, 
into  two  parts.     In  this  sense,  undoubtedly,   it  is 


I 


SUMMARIZING  THE  FACTS  105 

more  accurately  described  as  a  partition  expression 
or  division  mark,  although  it  serves  the  purpose  of 
an  average.  Similarly,  it  is  possible  to  divide  a  series 
into  more  than  two  parts.  In  case  the  division  is 
into  four  parts,  the  partition  expressions  are  known 
as  quartiles. 

What  are  the  characteristics  of  the  median? 

First. — In  its  computation,  all  of  the  data  are 
required,  but  the  frequencies  only  are  important  and 
not  the  size  of  the  items,  except  at  or  near  the  middle. 

Second. — It  is  uncertain  and  indefinite  in  a  series 
which  is  not  essentially  homogeneous.  That  is,  a 
series  may  be  uniform  throughout,  as,  for  instance, 
in  the  case  of  the  wage-rates  of  a  group  of  100  indi- 
viduals. The  median  of  such  a  series  would  be  the 
characteristic  wage-rate;  as  would  also  the  arithmetic 
mean.  However,  if  a  few  poorly  paid  individuals 
were  introduced  at  the  lower  side,  and  a  few  highly 
paid  persons  at  the  upper  side,  the  median  would 
remain  the  same,  but  the  arithmetic  mean  would  be 
different. 

Third. — ^The  median  may  be  computed  when  the 
size  of  the  items  at  the  extremes  is  unknown,  pro- 
vided the  frequencies  are  given.  This  is  of  distinct 
advantage  when  the  measurements  are  imperfect,  or 
incapable  of  being  known. 

Fourth. — The  median  may  be  indeterminate.  It 
may  fall  between  two  measurements  in  a  series.  In 
such  a  case,  it  is,  like  the  arithmetic  mean,  a  purely 
fictitious  number. 

If  business  men,  in  their  attempt  to  summarize 
the  detailed  facts  of  their  business,  would  use  both 
the  arithmetic  mean  and  the  median,  there  would  be 


106  STATISTICS  IN  BUSINESS 

less  tendency  for  their  generalizations  to  be  loose 
and  indefinite,  since  the  two  figures  would  supplement 
each  other.  However,  the  median,  because  of  its 
peculiar  meaning,  is  frequently  unconsciously  used. 
"Wage  earners,  for  instance,  are  ranked  according  to 
their  honesty,  integrity,  and  industry;  and  standards 
are  set  which  apply  not  to  the  exceptionally  good 
man,  nor  to  the  exceptionally  poor  man,  but  rather 
to  the  middle  man,  thought  of  in  comparative  terms. 
Psychologists,  in  the  selection  of  employees  by  mental 
tests,  or  by  other  means,  frequently  employ  the 
median,  and  relate  individuals  in  a  series  to  this 
middle  man.  Wherever  the  ranking  device  is  em- 
ployed, the  median  concept  is  used. 

Moreover,  the  arithmetic  mean  and  the  median  of 
details  which  are  not  too  erratic  and  dissimilar  tend 
closely  to  agree.  The  arithmetic  mean,  because  of  its 
being  affected  by  the  extremes  as  well  as  by  the  fre- 
quencies, tends  to  be  less  than  the  median  when  the 
small  items  predominate,  and  larger  than  the  median 
when  large  ones  are  more  frequent. 

If  the  arithmetic  mean  wage,  or  cost,  is  compared 
not  only  with  the  median,  but  also  with  the  quarter 
measures,  or  quartiles,  then  as  a  summary  expression, 
it  becomes  more  significant  than  when  it  stands  alone. 
The  point  was  made  in  the  discussion  of  the  arithmetic 
mean,  that  it  lacks  definiteness,  and  is  often  used 
loosely  to  describe  a  situation  which  cannot  be  sum- 
marized in  a  single  figure.  If  it  is  compared  with  the 
median  and  quartiles,  as  averages,  then  a  part  at  least 
of  this  criticism  no  longer  applies.  If  the  business 
executive  keeps  in  mind  the  purposes  which  averages 
'  serve,  and  the  necessity  for  business  facts  to  be  sum- 


SUMMARIZING  THE  FACTS 


107 


marized  in  brief  form,  he  should  be  anxious  to  employ- 
not  only  one  but  several  devices  which  serve  his 
purpose. 

The  use  of  the  median  in  connection  with  an  ordi- 
nary payroll  may  be  illustrated,  the  purpose  of  the 
average  (the  median)  being  to  characterize  the  hourly 
wage-rates  which  are  paid.  The  number  of  men  and 
the  wage-rates  per  hour  are  given  below : 

Table  10. — Table  Showing  Distribution  op  Hourly  Wage-rates 


Number  of  men 

Wage-rates  per 
hour,  cents 

Number  of  men 

Wage-rates  per 
hour,  cents 

12 
16 
25 

60 
70 
75 

9 
4 
2 

82 
90 
95 

The  arithmetic  wage-rate  is  73.6  cents  and  the  median 
75  cents.  It  will  be  noticed  that  the  order  of  arrange- 
ment is  consecutive,  and  that  the  median  rate  is  1.4 
cents  more  than  the  average.  The  wage-rate  of  the 
individual  one-quarter  of  the  way  up  the  series  is  70 
cents  and  that  of  the  individual  three-quarters  of  the 
way  up  the  series  is  75  cents.  In  the  median  and 
two  quartiles,  therefore,  we  have  three  summarizing 
expressions  of  this  series.  The  arithmetic  mean,  on 
the  other  hand,  gives  us  but  one. 

There  is  still  another  average,  which  is  in  current  use, 
and  which  should  be  employed  in  business.  It  is 
what  is  called  the  mode.  It  is  that  item  in  a  series 
which  is  most  characteristic,  or  common.  It  is  the 
typical  fact,  and  being  typical,  is  representative.  It 
is  in  no  sense  hypothetical  or  unreal.  It  is  that  posi- 
tion .where  most  of  the  instances  fall,  and  which  may 


108  STATISTICS  IN  BUSINESS 

be  said  to  be  characteristic.  In  the  above  series  show- 
ing the  wage-rates  for  men,  more  individuals  were 
shown  to  have  been  receiving  75  cents  than  any  other 
amount;  75  cents  is,  therefore,  the  mode.  Of  course, 
there  were  people  receiving  more  and  others  receiving 
less  than  this  amount,  but  these,  for  the  purpose  of 
this  particular  summarizing  expression  are  ignored. 

What  are  the  characteristics  of  the  mode  as  an 
average? 

First. — Only  a  part  of  the  data  is  required  for  its 
computation.  In  the  series  above,  the  mode  would 
have  been  no  different  had  the  two  people  who  are 
shown  to  have  received  95  cents,  received  $2.00. 
Similarly,  it  would  have  remained  the  same  had  the 
twelve  people,  who  are  shown  to  have  received  60  cents. 
per  hour,  received  purely  a  nominal  sum. 

Second. — The  mode  as  an  average  is  invariably  rep- 
resented in  a  series. 

Third. — In  the  calculation  of  the  mode,  the  frequen- 
cies, or  number  of  instances,  are  primary,  and  the  units 
to  which  the  frequencies  occur,  only  secondary. 

In  the  discussion  of  business  success  and  failure, 
labor  force,  cost,  etc.,  when  these  are  summarized  in  a 
single  expression,  undoubtedly,  the  mode  is  the  average 
which  is  most  commonly  in  mind.  The  modal  idea  is 
expressed  in  the  "average"  clerk,  the  "average"  bank 
clearing,  the  "average"  day's  sale,  the  "average" 
man  on  the  street.  That  is,  the  thing  which  is  the 
rule,  or  which  is  characteristic,  is  expressed  in  this 
way.  It  is  the  prevailing  rate,  or  individual,  which  is 
in  mind. 

Fourth. — Extreme  items  are  ignored. 


SUMMARIZING  THE  FACTS  109 

Fifth. — Its  location  is  sometimes  indeterminate. 
There  may  be  more  than  one  mode,  in  case  the  series 
is  complex. 

The  mode,  like  the  median,  is  different  from  the 
arithmetic  mean,  inasmuch  as  extreme  items,  or  in- 
stances, are  ignored.  The  mode  tends  to  remain  fixed, 
is  less  erratic  than  the  median,  and  far  less  subject 
to  change  than  the  arithmetic  mean.  When  taken  to- 
gether, these  three  averages  serve  rather  fully  to 
describe  the  detail  concerning  any  business  fact. 
Taken  alone,  either  of  them  is  indefinite  and  a  poor 
substitute  for  the  detail  which  they  replace. 

There  is  no  reason  why  business  should  not  become 
as  familiar  with  the  use  both  of  the  median  and  the 
mode,  as  it  is  with  the  arithmetic  mean;  and  there  is 
far  greater  justification  in  many  instances  for  the  use 
of  the  mode  as  a  single  expression,  than  there  is  for  the 
use  of  the  arithmetic  mean.  The  business  executive 
should  not  ''rush  headlong,"  as  it  were,  into  the  use 
of  any  of  these  averages,  without  an  appreciation  of 
the  relationship  which  they  have  to  his  precise  problems, 
and  without  a  keen  appreciation  of  the  characteristics 
which  each  possesses.  Each  of  them  is  designed  to  put 
into  brief  form,  for  the  purpose  of  comparison,  the 
essence  of  the  detail  to  which  it  relates.  They  should 
be  used  to  give  expression  to  a  conclusion  arrived  at 
from  the  study  of  details,  and  this  cannot  be  done  un- 
less the  precise  nature  of  each  one  is  thoroughly  under- 
stood. To  employ  averages  to  express  the  result  of  a 
process  of  thought  or  analysis,  is  always  legitimate 
when  they  are  used  discriminatingly. 

No  single  average  is  good  for  all  purposes.  Each  is 
affected  differently  by  the  arrangement,  frequencies. 


110  STATISTICS  IN  BUSINESS 

and  the  character  of  the  details,  and  should  be  em- 
ployed with  a  full  knowledge  of  its  peculiarities.  The 
use  of  an  average  is  always  a  function  of  the  purpose 
which  one  has  in  mind.  The  form  of  the  average  and 
its  use  cannot  be  divorced.  Caution  and  foresight  are 
necessary  at  every  step  in  the  use  of  averages;  caution 
as  to  those  which  are  to  be  employed;  foresight  as  to 
the  significance  which  they  have,  and  analysis  as  to 
the  possibility  of  details  to  be  characterized  in  such  a 
manner.  To  use  them  blindly,  and  without  discrimi- 
nation, is  in  violation  of  the  underlying  principles 
of  scientific  method  as  applied  to  business  problems. 
The  executive,  no  matter  how  large  or  how  small  the 
business  he  controls  may  be,  or  in  whatever  fields  he 
may  be  working,  cannot  afford  to  base  his  judgment 
on  averages  without  a  keen  appreciation  of  what  is 
implied  in  doing  so. 

In  the  use  of  averages  for  business  purposes,  the 
following  questions  should  be  raised  and  answered. 
Is  it  possible  to  employ  a  single  expression  to  depict 
the  details  which  are  essential  so  as  to  view  data  in 
all  their  bearings?  In  the  problem  considered,  is  the 
greatest  interest  in  the  characteristic  or  modal  feature, 
in  the  median  or  half-way  position  or  in  that  mathe- 
matical position  at  which  the  average  (arithmetic 
mean)  falls?  Is  it  necessary  and  wise  to  employ  all 
of  these  descriptive  units,  to  compare  their  differences 
and  to  determine  their  similarities?  No  single  an- 
swer to  these  questions  can  be  given.  To  employ  an 
average  may  be  legitimate,  and  still  the  question  be 
indeterminate  as  to  the  most  appropriate  average  to 
use.  Data  must  be  analyzed  and  the  functions  of 
averages  in  general  and  in  particular  be  clearly  per- 


SUMMARIZING  THE  FACTS  111 

ceived  before  answers  can  be  given.  As  caution  and 
analysis  are  necessary  in  the  use  of  averages,  so  dis- 
crimination and  judgment  are  essential  in  assigning 
importance  to  them  when  used. 

In  no  other  aspect  of  business  is  the  employment  of 
an  average  so  common  and  at  the  same  time  its  use 
so  little  understood,  as  in  summarizing  prices.  Sum- 
maries are  wanted  for  prices  of  labor,  money,  mate- 
rials, securities,  etc.  To  know  the  market  condition 
and  trend  is  imperative  for  business  operation  and 
planning.  But  prices  differ  for  different  goods  or 
services,  different  conditions  of  demand  and  supply, 
different  markets,  different  conditions  of  sale  and 
purchase.  The  meaning  of  price  change  is  different 
for  differently  situated  producers,  consumers,  and 
middlemen.  For  instance,  an  economist  may  use 
stock  prices  "to  measure  change  in  the  purchasing 
power  of  money  over  stocks;  a  speculator  may  wish 
to  forecast  the  probable  future  course  of  the  market; 
a  public  commission  may  be  interested  in  the  terms 
on  which  corporations  can  raise  new  capital;  a  pub- 
licist may  investigate  the  claim  that  government  regu- 
lation has  brought  loss  upon  investors;  a  financial 
historian  may  wish  to  mark  off  periods  of  expansion 
and  contraction;  a  trustee  may  inquire  whether  the 
fluctuations  of  his  security  holdings  have  compared 
favorably  with  the  average  course  of  the  market;  an 
insurance  company  may  seek  light  on  the  probable 
future  of  interest  rates;  a  student  may  wish  to  com- 
pare stock  speculations  with  the  price  fluctuations  of 
commodities  at  wholesale  or  retail,  of  labor,  of  bonds, 
of  farm  lands,  of  securities  in  other  countries,  etc. 
Now,  each  of  these  people  will  have  use  for  a  stock 


112  STATISTICS  IN  BUSINESS 

index.  But  the  more  carefully  these  various  uses  are 
analyzed,  the  clearer  it  becomes  that  their  require- 
ments differ."  The  prices  of  commodities,  wholesale 
and  retail,  are  wanted  for  as  varied  uses,  as  are 
also  those  of  the  prices  of  labor.  How  are  prices 
to  be  summarized  and  interpreted  for  these  different 
purposes? 

Business  men  and  students  of  economics  are  famil- 
iar with  the  currently  compiled  indexes  of  prices.  They 
at  least  know  by  name  Bradstreefs,  Dun's,  The  An- 
nalist's and  the  Bureau  of  Labor's  index  numbers. 
But  do  they  know  what  they  contain,  what  they  mean, 
and  are  they  consistent  in  their  use  of  them  in  con- 
nection with  price  problems?  Is  their  attitude  toward 
them  scientific,  or  rule-of-thumb?  How  discriminat- 
ing are  they  in  quoting  authorities,  and  how  consist- 
ent in  using  them  as  a  basis  for  business  policies  and 
conclusions? 

Index  numbers  in  the  simplest  form  may  be  defined 
as  relative  or  percentage  numbers  in  which  data  for 
one  year  or  other  similar  period,  or  an  average  for  a 
year  or  such  period,  are  taken  as  a  base,  generally 
indicated  by  100,  and  upon  which  data  for  subsequent 
years  or  periods  are  computed  as  percentages.  The 
method  by  which  a  simple  index  number  of  prices 
may  be  calculated  is  illustrated  below. 

What  has  been  the  movement  of  the  prices  of  build- 
ing material  during  the  war?  In  this  illustration, 
only  a  few  quotations  are  taken,  and  the  index  num- 
bers would  not  suffice  for  too  broad  a  generalization. 
However,  it  is  the  principle  of  index  number  making 
which  is  now  being  discussed  and  these  prices  will 
suffice  for  this  purpose. 


SUMMARIZING  THE  FACTS 


113 


Table  11. — Absolute  and  Relative  Wholesale  Prices  op  Build- 
ing Materials,  1913  to  1919^ 

Actual  Prices 


Commodity  quotation 

Average  wholesale  prices  in 

group 

1913 

1914 

1915 

1916 

1917 

1918  . 

1.  Clay  Products 

(o)  Brick,  Common  Build- 

ing   (New  York  City) 

per  M 

$6.6300'«5  84f57 

$5.9425 

J7.7267 

$8.8933 

$10.8975 

^6)  Sewer  pipe,  salt  glazed 

fire  clay,  6  in.   (N.   E. 

U.  S.)  per  linear  ft 

0.0558    0.0633 

0.0638    0.0704 

0.0750 

0.0800 

2.  Quarry  Products 

(c)  Indiana     Lime     stone. 

buff,  rough  block  (U.  S.) 

per  cu.  ft 

0.2500    0.2500 

0.2500    0.2625 

0.3583 

0.4208 

(d)  Lime  in  bulk  (Chicago) 

per  short  ton 

4  .3750 

4  .0000 

3.5000    4  37.'50 

6.1667 

7 .  2500 

3.  Cement 

(e)  Portland  cement  (N.  Y. 

and  N.  Eng.  States)  per 

bbl 

1.0442 

1 .0500 

0.8142 

1.0342 

1 .3358 

1 .6733 

CO  Portland  cement   (111.) 

per  bbl 

0.9906 

0.9052 

0.8821 

1.1144 

1 .3975 

1 .5500 

4.  Glass 

(g)  Window    glass,    single 

united,     inches,     40-A 

(N.  Y.)  per  50  sq.  ft 

2.5500 

2.55P0 

2.8050    3.4650 

4.5353 

6.7903 

5.  Lumber 

(A)  Southern   yellow   pine. 

Finish   B,   and   better, 

J 

6  in.  and  wider   (Ala., 

Ark.,  La.,  Tex.,  Miss.) 

per  M.  ft 

25.0312 

23.2227 

22.0422 

24.6016 

33.6094 

37 .8906 

(»)  Eastern  hemlock.  No.  1 

boards,  S-l-S,  1"  X  8", 

16'  (Mich,  and  Wis.)  per 

M.  ft 

20.4445 

18.8333 

18.1667 

21 .4792 

27.6458 

31  .1042 

6.  Paints 

0)  Paint     pigments,     dry 

colors,  ocher  (N.  Y.)  per 

ton 

12.0000  12  0000 

13.0000 

18.8333 

21 .3333 

30.0000 

'  Price  Bulletin  (various)  War  Industries  Board,  Washington,  D.  C, 
1919. 


114 


STATISTICS  IN  BUSINESS 

Relative  Prices 
1913  =  100 


Total  of  relatives 

1000.0 

969.9 

946.2 

1155.4 

1447.1 

1778.4 

Index  numbers  as  averages  of 
relative  prices 

100.0 

97.0 

94.6 

115.5 

144.7 

177.8 

100.0 
100.0 
100.0 
100.0 
100.0 
100.0 
100.0 
100.0 
100.0 
100.0 

8S.2 
113.5 
100.0 

91.4 
100.5 

91.4 
100.0 

92.8 

92.1 
100.0 

89.6 

114.3 

100.0 

80.0 

78.0 

89.0 

110.0 

88.1 

88.9 

108.3 

116.5 
126.2 
105.0 
100.0 

99.0 
112.5 
135.9 

98.3 
105.1 
156.9 

134.1 
134.5 
143.3 
141.0 
127.9 
141.1 
177.9 
134.3 
135.2 
177.8 

164.4 

143.4 

168.3 

165.7 

160.2 

156.5 

266.3 

151.4 

152.2 

250.0 

According  to  this  calculation,  prices  of  building 
materials  for  the  years  1913  to  1918  inclusive,  ad- 
vanced as  follows: 


Index  number 

Per  cent,  increase 

Year 

Over  1913 

Over  preceding  year 

1913 

100.0 
97.0 
94.6 
115.5 
144.7 
177.8 

3.0* 

5.4* 
15.5 
44.7 
77.8 

1914 

3.0* 

1915 

2.5* 

1916 

22.1 

1917 

25.3 

1918 

22.9 

*  Decrease. 

This  simple  example  contains  the  essential  steps  in 
the  calculation  of  an  average  of  relative  prices  type  of 
index  number.  More  important  than  the  arithmetical 
calculation  is  the  selection  of  prices  or  other  data  to  be 
compared.  Indeed,  this  is  the  major  consideration 
in  making  index  numbers.     After  all,  the  purpose  in 


SUMMARIZING  THE  FACTS  115 

calculating  them  is  to  make  a  comparison,  and  the 
validity  of  the  inference  drawn  from  them  is  deter- 
mined not  only  by  the  method  in  which  they  are  com- 
bined, but  also  by  the  fact  of  their  inherent  likeness. 
The  truth  that  like  can  be  compared  only  with  like 
applies  here  with  especial  emphasis. 

In  calculating  and  using  an  index  number,  busi- 
ness executives  should  have  in  mind : 

First. — The  purpose  for  which  the  results  are  to  be 
used. 

Second. — The  number  and  kind  of  commodities 
that  are  to  be  included,  the  form  in  which  their  prices 
are  stated,  and  the  markets  from  which  the  quota- 
tions are  secured. 

Third. — The  questions  as  to  whether  all  commodi- 
ties are  to  be  treated  as  equal,  or  are  to  be  given 
different  weights. 

Fourth. — The  test  to  be  used  in  assigning  different 
weights. 

Fifth. — The  base  period  against  which  comparisons 
are  to  be  made. 

Sixth. — If  averages  of  relative  prices  are  used,  the 
average  which  should  be  chosen. 

These  conditions  are  important  since  not  all  index 
numbers  are  equally  well  suited  for  all  purposes.  If 
an  executive  wishes  to  calculate  the  effect  on  his  em- 
ployees of  the  increased  cost  of  living,  he  ought  not 
to  choose  wholesale  prices  as  a  basis  for  an  index  series. 
Moreover,  the  number  of  commodities  which  enter  into 
the  index  numbers  and  the  importance  assigned  to 
them,  for  this  purpose,  are  important.  Prices  of  a 
half-dozen  commodities  purchased  in  large  quantities 
by  consumers  are  far  more  important  than  several 


116  STATISTICS  IN  BUSINESS 

times  this  number  which  enter  only  insignificantly  into 
living  costs.  The  same  consideration  is  equally  true 
in  the  construction  of  a  wholesale  series,  a  cost  of  pro- 
duction series,  and  a  securities  series. 

Moreover,  the  collection  of  prices  and  use  of  index 
numbers  are  difficult  in  another  way.  There  are 
producers'  and  consumers'  prices,  jobbers'  and  mill 
prices,  wholesale  and  retail  prices.  There  are  prices 
in  large  markets  under  conditions  of  world  competi- 
tion, and  prices  in  isolated  communities  where  mo- 
nopoly essentially  rules.  The  selection  of  prices  raises 
such  questions  as  the  following: 

What  is  meant  by  price;  is  the  price  retail  or  whole- 
sale; under  what  condition  is  price  named;  to  what 
grade  of  commodity  or  service  does  it  apply;  on  what 
market  is  it  quoted;  are  "prices"  contract,  import  or 
freely  competitive  in  character? 

Now,  there  are  various  ways  in  which  index  numbers 
may  be  computed.  A  simple  form  is  illustrated  on 
pages  113-114.  In  this  case,  1913  is  taken  as  a  base. 
The  prices  are  calculated  as  relatives  or  percentages 
on  this  year  and  the  percentages  averaged.  But 
neither  a  base  nor  an  average  is  necessary.  Actual 
prices  may  be  reduced  to  a  common  denominator,  as 
so  much  per  pound,  and  simply  added  together. 
The  result  is  a  series  of  amounts  in  dollars  and  cents. 
It  is  in  this  form  in  which  Bradstreet's  number  is 
calculated.  Bradstreet's  numbers  for  recent  years 
are  given  in  Table  12. 

The  Annalist  index  number  is  different.  It  is  a 
weekly  number  made  from  the  wholesale  prices  of 
twenty-five  commodities  chosen  in  such  a  way  as  to 
represent  the  principal  items  in  a  family  budget.     It 


SUMMARIZING  THE  FACTS 


117 


Table  12 — Table  Giving  BKADSTKEtT's  Commodity  Price  Index 
Numbers,  January,  1903  to  July,  1919 


Index  number;  first  of  the  month 

Year 

January 

April 

July 

October 

1903 

$8.0789 

7.9885 

8.0827 

8.3289 

8.9172 

8.2949 

8.2631 

9.2310 

8.8361 

8.9493 

9.4935 

8.8857 

9.1431 

10.9163 

13.7277 

17.9436 

18.5348 

$8.1247 

7.9690 

7.9996 

8.2987 

8.9640 

8.0650 

8.3157 

9.1996 

8.5223 

9.0978 

9.2976 

8.7562 

9.7753 

11.7598 

14.5769 

18.4431 

17.2795 

$7.8706 

7.6318 

7.9160 

8.2835 

9.0409 

7.8224 

8.4573 

8.9246 

8.5935 

9.1119 

8.9521 

8.6566 

9.8698 

11.5294 

16.0680 

19.1624 

18.8964 

$7 . 9083 

1904 

7  9213 

1905 

8  2298 

1906 

8  5580 

1907 

8 . 8506 

1908 

8  0139 

1909 

8  7478 

1910 

8.9267 

1911 

8  8065 

1912 

9.4515 

1913 

9.1526 

1914 

9.2416 

1915 

9  9774 

1916 

12  0399 

1917 

16  9135 

1918 

18  9942 

1919 

19.5215 

Table   13. — Table   Giving  the   Annalist's   Yearly   Commodity 

Price  Index  Numbers,  1890  to  September,  1919 

(Base  period  1890  to  1899  =  100) 


Year 

Index 
number 

v„__               Index 
^^^"^             number 

Year 

Index 
number 

1890 

1891 

1892 

109.252 

119.488 

108.624 

116.100 

102.076 

94.604 

80.096 

84.092 

92.208 

93.348 

1900 

1901 

1902 

1903 

1904 

1905 

1906 

1907 

1908 

1909 

99.388 
104.656 
116.264 
107.516 
108.664 
110.652 
114.364 
117.940 
125.756 
133.952 

1910 

1911 

1912 

137.172 
131.068 
143.254 

1893 

1913 

139.980 

1894 

1914 

146.069 

1895 

1915 

148  055 

1896 

1916 

175 . 720 

1897 

1917 

261 . 796 

1898 

1918 

287 . 080 

1899 

1919  to  Sept.  1 

301.904 

118 


STATISTICS  IN  BUSINESS 


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SUMMARIZING  THE  FACTS  119 

is  calculated  as  an  average  of  relatives,  as  is  the  ex- 
ample on  pp.  113-114,  but  uses  as  a  base  the  average 
of  the  prices,  1890-1899.  The  yearly  numbers  for  the 
years  since  1890  appear  in  Table  13. 

In  Table  14  a  number  of  American  and  foreign 
wholesale  price  index  series  have  been  reduced  to  a 
common  base  by  dividing  the  index  in  each  series 
for  1913,  on  the  original  base,  into  the  index  for  each 
year  or  month  on  that  base.  For  some  of  the  series 
this  process  gives  only  approximately  correct  results, 
but  these  are  sufficiently  accurate  for  general  purpose 
comparisons. 

The  most  satisfactory  index  number  of  retail 
prices  for  the  measurement  of  the  changing  prices  of 
foods  is  that  compiled  by  the  United  States  Bureau 
of  Labor  Statistics.  This  series  is  shown  in  the 
following  ratio  chart  for  the  years  1913-1919. 

The  principal  peculiarities  of  index  or  relative 
numbers  of  prices  may  be  summarized  as  foUows: 

First. — " No  index  number  corresponds 

to  a  real  thing An  index  number  points  to 

no  single  fact.     It  gives only  an  indication 

of  a  general  trend.  People  often  think  and  speak 
loosely  on  this  topic,  as  if  an  index  number  told  the 
whole  story  once  for  all.  There  is  no  one  change  in 
prices.  There  is  a  medley  of  changes,  different  in 
direction  and  degree.  All  that  we  can  hope  to  secure 
by  averaging  and  summarizing  is  some  concise  state- 
ment of  the  general  drift." 

Second. — ^Index  numbers  ot  wholesale  and  retail 
commodities  should  be  distinguished.  The  conditions 
under  which  wholesale  and  retail  prices  are  deter- 


120 


STATISTICS  IN  BUSINESS 


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SUMMARIZING  THE  PACTS  121 

mined  are  different,  as  are  also  the  uses  to  which  they 
should  be  put. 

Third. — For  any  index  number  the  types  of  the 
commodities  which  are  used  are  significant.  Dis- 
tinction should  be  made,  for  instance,  in  wholesale 
index  series,  between  producers'  and  consumers' 
goods;  between  raw  and  manufactured  commodities; 
between  mineral,  animal,  and  farm  products.  All  of 
these  respond  differently  to  conditions  of  scarcity  and 
surplus,  and  time  and  place. 

Fourth. — In  using  index  numbers  consideration 
should  be  given  to  the  number  of  commodities  used, 
the  places  from  which  quotations  are  taken,  and  the 
frequency  with  which  they  are  included. 

Fifth. — Index  numbers  of  prices  should  be  con- 
sidered from  the  point  of  view  of  the  method  by  which 
they  are  computed.  In  this  respect  the  following  are 
important. 

(a)  Are  the  numbers  average  prices  or  actual  prices? 
If  average  prices,  what  average  is  used  and  with  what 
effect? 

(6)  Are  the  commodities  taken  as  of  equal  impor- 
tance, or  are  some  commodities  assigned  greater 
importance  than  others? 

(c)  If  weights  are  assigned  to  indicate  relative 
importance,  upon  what  basis  are  they  chosen? 

{d)  If  a  base  year  is  used,  what,  if  any,  significance 
is  there  in  the  period  chosen? 

Sixth. — General  purpose  should  not  be  confused 
with  special  purpose  index  numbers  of  prices. 

Other  phases  of  index  numbers  of  prices  are  impor- 
tant to  the  business  executive,  but  they  cannot  be 
treated  here.     For  a  fuller  discussion  of  them,  the 


122  STATISTICS  IN  BUSINESS 

reader  may  consult  the  author's  Introduction  to 
Statistical  Methods. 

Now,  what  are  some  of  the  inconsistencies  of  which 
the  business  man  and  others  are  guilty  in  the  use  of 
price  index  summaries?  There  are  many,  but  only  a 
few  will  be  suggested  here. 

First. — The  demand  for  wage  increase  is  brought 
to  a  head  in  a  strike,  and  justification  is  sought  by 
labor  in  the  increased  cost  of  living.  The  business 
man  consults  a  price  index  series,  but  unfortunately, 
he  chooses  the  wrong  one.  It  may  be  BradstreeVs, 
or  the  Bureau  of  Labor  Wholesale  series  to  which  he 
refers,  and  from  which  he  develops  his  argument. 
He  is  in  error,  {a),  in  choosing  a  wholesale  series; 
(6),  in  construing  the  change  of  prices  as  indicated 
as  equivalent  to  cost  of  living  changes;  (c),  in  choosing 
a  general  purpose  series  and  using  it  for  a  particular 
use;  {d),  in  failing  to  see  that  the  weights  assigned  to 
commodities  have  nothing  to  do  with  the  scale  in 
which  the  commodities  enter  into  consumers'  budgets. 

Second. — Need  arises  for  some  measure  of  the  whole- 
sale prices  of  manufactured  producers'  goods,  such,  for 
instance,  as  farm  or  other  machinery.  The  Annalist 
index  number  is  used,  notwithstanding  the  fact  that 
68  per  cent,  of  the  manufactured  commodities  con- 
tained in  this  number  are  consumers'  rather  than 
producers'  goods,  and  that  32  per  cent,  of  the  com- 
modities are,  in  fact,  raw  rather  than  manufactured 
materials. 

Third. — Similarly,  an  index  number  is  wanted  which 
will  serve  as  a  general  barometer  of  business,  and 
Dun's  is  chosen,  notwithstanding  the  fact  that  it  is 
given  as  the  amount  in  dollars  and  cents  which  is 


SUMMARIZING  THE  FACTS  123 

required  to  purchase  a  year's  supply  of  goods  for  an 
individual  at  a  given  time,  and  is  not  as  susceptible 
to  market  changes  in  prices  as  is  Bradstreet's  or  the 
Bureau  of  Labor's  wholesale  number. 

It  is  unnecessary  to  give  further  examples  of  the 
unscientific  use  of  summarized  price  data.  The  above 
illustrations  undoubtedly,  are  of  daily  occurrence. 
Here,  fact  analysis  is  ignored,  and  the  scientific 
method  has  no  place. 

Business  facts  must  be  summarized  and  digested, 
and  averages  are  useful  in  the  process,  whether  applied 
to  prices,  wages,  costs,  sales,  or  what  not.  The 
process  of  summarization,  however,  is  fundamental, 
and  the  spirit  in  which  it  is  done,  exacting.  The 
technique  is  important  here  as  it  is  in  tabulation  and 
graphics,  and  it  is  hoped  that  what  has  been  said  will 
at  least  serve  the  purpose  of  emphasizing  the  scientific 
attitude  in  which  the  technique  should  be  applied, 
and  of  describing  briefly  the  w^ays  in  which  detail 
may  be  summarized. 


CHAPTER  VII 

COMPARISON  AND  THE  ESTABLISHMENT  OF 
BUSINESS  PRINCIPLES  AND  STANDARDS 

The  modern  business  executive  must  see  business 
facts  and  relations  in  their  larger  aspects.  Business 
is  intensely  human.  It  deals  in  the  last  instance 
with  individuals  and  with  groups,  and  the  psychology 
of  both  must  be  understood.  Moreover,  the  fact 
must  be  appreciated  that  the  time,  place,  and  condi- 
tion under  which  business  is  carried  on,  are  vital  in 
the  comparisons  which  are  made,  the  standards  which 
are  set  up,  and  the  principles  which  are  established. 
Business  is  controlled  by  customary  and  statutory 
law,  as  well  as  by  its  legal  interpretation.  The  in- 
stitutions of  property,  custom,  and  contract  also 
affect  business  at  every  turn,  and  its  plans  must  be 
interpreted  in  the  light  of  them.  Similarly,  political 
ideals  are  potent  in  shaping  the  sphere  which  business 
assumes,  and  in  controlling  its  development.  Compe- 
tition is  also  an  important  factor  and  the  exercise  of 
personal  initiative  important.  These  larger  facts  and 
relationships  cannot  be  ignored. 

Just  how  these  larger  aspects  of  business  are  signi- 
ficant must  be  determined  upon  an  analysis  of  each 
tjrpe  of  enterprise,  and  the  nature  of  its  immediate 
problems.  Custom  may  control  in  the  determination 
of  the  prices  of  goods  and  services,  and  in  the  wages 
which   are   paid.     Statutory   law   may   control    the 

124 


BUSINESS  PRINCIPLES  AND  STANDARDS  125 

form  of  business  and  the  expenses  under  which  it 
operates.  In  the  latter  aspect,  taxes  and  other  pay- 
ments imposed  by  governments  are  instances  in  point. 
Concerning  them,  business  must  take  an  enlightened 
and  positive  attitude  and  provide  for  them  in  the 
accounts  which  are  kept  and  the  plans  which  are 
made.  Of  these  facts,  business,  of  course,  is  fully  a\Vare 
in  a  general  way  when  problems  arise,  but  it  does  not 
always  see  their  full  import  from  day  to  day  and 
make  provision  for  them. 

The  point  which  is  being  stressed  is  that  business 
must  be  considered  in  its  relative  aspects,  and  that 
those  w^ho  are  in  control  must  not  be  unmindful  of  its 
relationship  to  the  underlying  forces  of  economic, 
political,  and  social  life.  It  is  necessary,  of  course, 
to  see  one's  individual  problems,  and  to  settle  them 
with  regard  to  the  effect  which  the  solution  will  have 
on  profits,  on  public  approval,  and  on  the  interests 
of  those  who  are  instrumental  in  bringing  success. 
But  for  a  business  executive  solely  to  see  them  as  his 
problems,  and  to  treat  them  as  if  they  were  unrelated 
to  the  larger  political,  economic,  and  social  currents 
of  the  times,  is,  of  course,  to  lose  sight  of  the  factors 
which  at  bottom  make  them  problems  at  all.  If  this 
is  done,  the  solutions  offered  may  be  temporary  and 
bring  with  them  later  more  serious  and  fundamental 
problems,  the  solution  of  which  lies  outside  of  the  ken 
and  the  experience  of  the  individual  establishment. 
Tampering  with  the  labor  problem — putting  off  facing 
the  real  problems  by  refusing  to  meet  the  real  issues, 
or  by  ignoring  that  they  exist — for  instance,  is  a  case 
in  point.  This  problem  is  far  larger  than  any  estab- 
lishment, and  its  issues  more  fundamental  than  those 


126  STATISTICS  IN  BUSINESS 

which  are  the  subject  of  controversy  within  a  given 
industrial  concern.  How  this  problem,  like  others,  is 
related  to  group  psychology,  to  political  and  social 
ideas,  and  how  it  may  be  constructively  met,  must  be 
determined  by  business  if  it  is  to  function  smoothly 
and  the  cooperation  upon  which  it  rests  is  to  endure. 

Although  the  problems  of  business  are  relative  to 
time,  place,  and  condition,  and  are  intimately  related 
to  such  institutions  as  custom,  property,  and  con- 
tract, and  to  problems  of  psychology,  many  of  them 
may  be  stated  in  definite  terms  and  the  facts  which 
define  and  measure  them  be  determined.  What  these 
facts  are,  the  conditions  which  must  be  established  in 
order  to  measure  them,  and  the  ways  in  which  they 
may  be  summarized  have  been  suggested  in  the  pre- 
ceding pages.  What  must  now  be  emphasized  are  the 
conditions  which  make  comparisons  and  the  establish- 
ment of  standards  and  principles  valid  for  business 
uses.  How  are  the  results  of  the  application  of  sci- 
entific methods  to  business  to  be  realized  and  made 
to  contribute  to  business  success? 

The  establishment  of  business  standards  and  princi- 
ples results  from  comparison.  For  things  to  be  com- 
pared, they  must  possess  points  in  common,  and  to 
determine  common  qualities,  uniform  standards  of 
measurements  must  be  applied.  A  business  fact, 
however,  is  not  a  uniform  thing;  it  does  not  always 
exhibit  itself  in  the  same  way.  It  cannot  always  be 
treated  uniformly  and  subjected  to  one  foot-rule.  It 
is  complex  and  varied  and  requires  that  the  units  of 
measurements  applied  to  it  shall  be  adjusted  according 
to  the  form  in  which  it  reveals  itself.  Hence,  com- 
parisons of  business  facts  are  never  perfect;  they  are 


BUSINESS  PRINCIPLES  AND  STANDARDS         127 

experimental  and  approximate.  The  standards  must 
constantly  be  changed  and  adapted  to  time,  place, 
and  condition.  Because  of  change  in  circumstances, 
what  is  true  today,  under  a  given  condition,  may  not 
be  true  tomorrow. 

If  comparisons  are  difficult  to  make  and  are  often 
misleading,  then  the  establishment  of  cause  and  effect 
relations  in  a  narrow  and  absolute  sense  is  virtually 
impossible.  It  is  a  tempting  thing  for  a  business 
executive  to  reason,  that  if  A  happens,  B  will  result. 
He  would  Uke  to  be  sure,  for  instance,  that  if  prices 
are  lowered,  sales  will  be  stimulated;  that  if  he  puts 
more  money  into  advertising,  larger  sales  will  be 
experienced;  that  if  he  grants  the  increase  of  wages 
demanded,  labor  will  be  satisfied.  Unfortunately, 
peace  of  mind  does  not  come  in  this  way;  a  quantita- 
tive cause  does  not  necessarily  bring  with  it  an  equal 
quantitative  effect.  The  result  is  not  absolute,  but 
relative.  Business  does  not  go  on  repeating  itself  in 
a  round  of  sameness,  nor  do  the  effects  of  certain 
causes  always  remain  identical.  Variation  is  always 
present. 

To  illustrate,  stimulation  of  business  is  shown  in 
increased  bank  clearings  and  in  expanding  loans,  but 
not  all  banks  are  equally  affected,  nor  is  business 
uniformly  speeded  up.  Surplus  reserves  of  banks 
are  related  to  interest  rates  on  call  loans,  but  will  an 
X  reserve  always  give  a  Y  rate?  A  change  in  whole- 
sale prices  causes  the  retail  prices  to  fluctuate,  but 
will  a  change  of  20  per  cent.,  for  instance,  in  the  whole- 
sale price  of  hides  always  bring  20  per  cent,  change  in 
the  price  of  shoes?  To  ask  such  questions  is  to 
answer  them ;  and  yet,  is  it  not  customary  in  business 


128  STATISTICS  IN  BUSINESS 

for  plans  to  be  made  and  policies  pursued  as  if  there 
were,  underlying  the  whole  business  structure,  some 
automatic  and  perfectly  certain  cause  and  effect 
machinery? 

Business  phenomena  are  related;  they  do  stand  in 
the  relationship  of  cause  and  effect  to  each  other,  but 
this  is  not  so  simple  and  so  predictable  as  it  is  some- 
times indicated  to  be.  What  the  relationship  is  can 
rarely  if  ever  be  guessed ;  but  it  can  be  measured,  and 
it  is  the  function  of  scientific  method  to  determine  it. 

There  is  a  Science  of  Business.  The  method  by 
which  it  is  discovered  and  stated  is  the  same  as  that 
which  is  employed  in  the  natural  sciences;  but  the 
difficulties  of  applying  it  are  vastly  more  serious. 
Experimentation  is  not  so  easy;  the  factors  which  are 
dealt  with  are  far  more  complex,  and  the  conditions 
under  which  they  operate  more  diverse  and  diflEicult  of 
standardization.  But  the  problem  of  understanding 
it  is  not  insuperable.  The  absolutely  indispensable 
conditions  upon  which  it  rests  are  first,  a  whole- 
some respect  and  an  unconditional  demand  for  the 
truth;  second,  scientific  observation  and  measure- 
ment of  business  facts;  third,  the  application  of  facts 
to  business  problems  upon  the  basis  of  working  hypo- 
theses, with  the  purpose  of  determining  their  relative 
truths;  and  fourth,  the  formulation  of  standards  and 
principles  as  rules  for  business  guidance. 

A.  business  synthesis  is  sadly  needed,  not  alone  of 
the  activities  of  individual  business  establishments, 
but  of  industries  as  well.  Such  a  synthesis  lies  within 
the  power  of  every  concern  and  of  industries  too,  the 
moment  that  it  is  seriously  wanted.  Fact  analysis 
supplies  the  method.     What  is  most  needed  is   a 


BUSINESS  PRINCIPLES  AND  STANDARDS  129 

disposition  seriously  to  employ  it  on  the  requisite  scale. 
Business  rivalry  and  diminished  profits  require  that 
business  be  scientific,  and  the  new  competition  sug- 
gests the  ways  in  which  savings  and  economies  may  be 
introduced.  What  is  needed  among  competitors 
is  common  statistical  activity  and  exchange  of  informa- 
tion. More  analysis  of  business  facts  and  equal 
sharing  in  the  results  are  necessary.  The  old  dogma, 
''the  gain  of  one  is  the  loss  of  another,"  needs  to  be 
abandoned.  Bureaus  of  research,  or  research  depart- 
ments, must  become  a  component  part  of  every 
business  establishment,  and  the  scientific  method  the 
point  of  view  of  every  business  executive. 

What  the  scientific  method  is  has  been  fully  de- 
scribed. What  the  facts  of  business  are  which  should 
be  analyzed  have  been  suggested,  and  the  ways  indica- 
ted in  which  complex  data  may  be  summarized.  Hav- 
ing caught  the  spirit  of  fact  analysis,  and  understanding 
what  it  implies,  it  is  the  indispensable  function  of  an 
executive  to  apply  it  to  his  problems.  Moreover, 
it  is  essential  for  employers^  organizations,  business 
clubs,  and  managers'  associations,  to  study  scientific 
method  in  relation  to  business  problems  and  to  install 
machinery  whereby  the  experiences  of  all  may  be  put 
at  the  service  of  each. 

When  businesses  have  done  this,  either  individually 
or  cooperatively,  industry  will  be  seen  in  a  new  light. 
The  principles  and  rules  for  guidance  then  will  not 
be  formulated  out  of  prejudice  nor  arrived  at  in  an 
occult  or  rule-of-thumb  manner,  but  will  be  established 
on  the  basis  of  facts  scientifically  analyzed  and  prop- 
erly interpreted.  They  will  not  be  accepted  blindly, 
but  with  discrimination,  and  the  conditions  will  be 


130  STATISTICS  IN  BUSINESS 

established  for  making  business  scientific.  Fact 
analysis  will  become  the  rule,  and  industry  will  prosper 
as  a  result  of  its  application.  The  standards  of  fact 
analysis  are  severe,  its  methods  are  exact,  but  the 
results  worth  while.  Business  must  be  conducted  on 
a  scientific  basis. 

There  are,  therefore,  in  summary,  two  phases  to 
scientific  method,  as  applied  to  business  or  other 
phenomena:  first,  scientific  observation,  and  second, 
logical  inference.  In  the  application  of  these  stand- 
ards, a  science  of  business  is  to  be  developed. 


INDEX 


Accidents,  16;  compensation  for,  16;  how  measured  statistically,  28; 
statistics  of,  and  comparability,  28. 

Accounting  and  Statistics,  3. 

Accuracy,  meaning  and  standards  of,  34-35. 

Advertising  and  custom,  36. 

Analysis,  business,  requirements  of,  3-4,  10,  12;  relation  of  comparison 
to,  30. 

Annalist's  index  number,  112;  1890  to  1919,  117;  how  calculated, 
116-117,  119;  peculiarities  of,  122. 

Average,  average  measure  the  best  measure,  103;  the  arithmetic 
mean,  100-104;  (arithmetic  mean),  characteristics  of,  101,  104; 
(arithmetic  mean),  how  computed,  101;  relationship  of  (arith- 
metic mean)  to  the  mode,  109;  concept  of,  97-99;  the  median 
(see  Median) ;  the  mode  (see  Mode). 

Averages,  as  summaries  of  details,  123;  choice  of,  for  business  analysis, 
109-110;  relation  of,  to  business  problems,  99-100,  102;  sampUng 
and,  102-104;  use  of,  to  summarize  prices,  111-112. 

B 

Babson  service,  22-23. 

Bank  clearings,  as  measure  of  trade  buoyancy,  29. 

Banking,  21. 

Bar-diagrams,  component  parts  and  (illustrated),  73;  order  of  detail 

and  (illustrated),  72,  73,  74, 
Bars,  component  parts  and  (illustrated),  74,  79,  80,  81;  constrasted 

with  surfaces  (illustrated),  75,  78;  cross-hatching  in  (illustrated), 

79;  position  of,  62;  use  of,  as  contrasted  with  lines  connecting 

bars  in  historical  series,  86-88;  use  of,  for  comparisons  of  size,  61; 

use  of  subdivided,  for  presenting  component  parts,  62;  use  of 

vertical,  in  frequency  distributions,  62. 
Base  lines  in  diagrams,  59. 
Bias,  31. 
Bradstreet's  index  number,  112;  how  calculated,  116;  1903  to  1919, 

117;  peculiarities  of,  122. 

131 


132  INDEX 

Brinton,  W.  C,  Graphic  Methods  for  Presenting  Fads,  68. 

Brookmire  Service,  22-23. 

Buildings,  23. 

Bureau  of  Labor  price  index  number,  112, 

Business,  a  "going"  concern,  36;  cause  and  effect  relations  in,  127-128; 
competition  and,  2;  facts  of,  classified,  5;  meaning  of,  1;  modern, 
contrasted  with  ancient,  2;  seen  by  different  interests,  1-2;  seen 
through  averages,  99-100;  the  science  of,  128;  uses  of  index 
numbers  in,  115-116. 

Business  advertising  and  custom,  36. 

Business  analysis,  cooperatively  undertaken,  129-130;  misuse  of 
index  numbers  in,  122-123;  questions  which  it  will  answer,  36-37 
scientific  method  and,  38-40;  scientific  method  in,  129-130 
scope  of,  125-126;  short-  and  long-time  influences  and,  34 
standards  and,  128;  steps  in,  128;  use  of  averages  in,  109-110 
use  of  tables  in,  54;  what  it  requires,  3-4,  8,  10,  12. 

Business  barometer,  Bradstreet's  index  number  a,  123. 

Business,  cooperative,  12;  custom  and,  124-125;  law  and,  124-125; 
pohtical  ideals  and,  124-125;  property  relations  and,  124-125. 

Business  facts,  capital,  8-9;  character  of,  27;  classified,  13;  commen- 
surable, 26;  credit,  9-10;  depreciation  rate,  11-12;  frequency  of 
measurement  of,  34;  investments,  9;  labor,  8;  land,  11;  land, 
classified,  14;  law  and  poUcy,  14;  market,  7;  market,  classified,  14; 
meaning  and  use  of,  29;  production,  6;  production,  classified,  13; 
profits,  10,  11;  sales,  7;  taxes,  11;  transportation,  classified,  14. 

Business  judgments,  crude  data  and,  30;  facts  and,  2;  general,  and 
statistical  facts,  29. 

Business  operations,  the  measurement  of  facts  and,  36. 

Business  policy,  shaped  through  analysis,  37-38. 

Business  problems,  relative  aspects  of,  126. 

Business  research,  36 

Business  records,  custom  and,  36. 

Business  standards,  statistical  analysis  and,  37. 

Business  synthesis,  how  realized,  128-129. 


Capital  facts,  8-9,  18-19;  classified,  13;  earnings,  18-19;  resources,  18. 

CapitaUzation  vs.  capital,  18. 

Cause  and  effect,  business  relations  in  the  order  of,  128. 

Census,  20. 

Circle  diagrams  to  represent  component  parts  (illustrated),  65-67. 

Classification,  relation  to  tabulation,  41. 


I 


INDEX  133 

Classification  of  facts,  41;  meaning  of,  41-42. 

Collection  of  data,  schedules  and,  51;  relation  of,  to  tabulation,  51. 

Color  diagrams,  61. 

Comparison,  essence  of,  126-127;  what  it  involves,  30. 

Comparison  in  business  analysis,  126-127. 

Competition,  business  analysis  and,  37. 

Component  parts,  choice  of  graphics  for  expressing,  61-62. 

Cooperation  in  business,  12. 

Cost  facts,  12. 

Cost  of  living,  sampling  and,  32;  choice  of  index  numbers  to  measure, 

115-116;  measurement  of,  32. 
Costs,  business  analysis  and,  36;  meaning  of  average,  99-100. 
Credit,  21. 

Credit  facts,  9-10,  14. 
Crops,  19. 

Cross-hatching,  for  presenting  component  parts,  62. 
Curves,  historical,  57-58;  scales  for,  57;  smoothing  of,  57;  use  of,  57. 

D 

Depreciation,  rate  of,  11-12. 

Diagrams,  arrangement  of  items  and,  60;  base  Unes  in,  59;  form  of,  and 

the  person  for  whom  designed,  64;  position  of  titles  in,  60-61; 

rules  for  general  make  up  of,  59-61;  scale  units  and,  59;  size  of 

sheets  and,  61;  surfaces  within  surfaces  and  (illustrated),  76-77; 

to  include  the  data  represented,  59;  use  of  colors  and,  61. 
Dot  Map,  frequency  (illustrated),  86;  use  of  frequency,  83;  varying 

shades  of  dots  in,  85;  (illustrated),  88;  varying  size  dots  in,  84; 

(illustrated),  87. 
Dun's  index  number,  112;  peculiarities  of,  122-123. 

E 

Earnings,  15,  18-19. 

Editing  of  schedules,  52-53. 

Executive,  attitude  of,  toward  problems,  27. 

Exports,  as  measure  of  trade  buoyancy,  29. 


Fact  analysis,  meaning,  3-4,  10,  12. 

Facts  of  business,  characteristics  of,  5;  classified,  5. 

Failures,  22. 

Forecasting,  22-23. 


134  INDEX 

G 

Graphic  forms,  choice  of,  61-64;  use  of,  for  comparisons  of  size,  61; 
use  of,  for  comparison  of  component  parts,  61-62;  use  of,  in 
frequency  distributions,  62;  use  of,  in  presenting  geographic 
variations,  62-63;  for  presenting  time  variations,  63-64. 

Graphics,  55-96;  appUcation  of,  to  business  analysis,  58;  contrasted 
with  tabulation,  55;  position  of  titles  on  graphs,  60-61;  principles 
covering  use  of,  56;  rules  for  selection  of,  55-56;  use  of  bars  in,  for 
comparisons  of  size,  61;  use  of  lines  in,  for  comparisons  of  size,  61. 

Graphs,  form  of,  and  the  person  for  whom  designed,  64;  historical, 
57-58,  63;  historical,  use  of  straight  lines  in,  63;  historical,  and 
vertical  zero,  64;  position  of  scales  in  historical,  64;  rules  for 
general  make  up  of,  59-61;  scales  for,  57;  size  of,  and  sheet,  61; 
smoothing  of,  57;  use  of,  57. 

H 

Harvard  Committee  on  Economic  Research,  23. 
Hollerith  tabulating  machines,  53. 


Income  tax,  returns,  49. 

Immigration,  17-18. 

Imports,  as  measure  of  trade  buoyancy,  29. 

Index  number,  Annalist's,  112;  Bradstreet's,  112;  Bureau  of  Labor, 
112;  Dun's,  112. 

Index  numbers,  calculation  of,  116;  certain  American  and  foreign, 
compared,  118;  defined,  112;  method  of  calculation  of ,  illustrated, 
112-114;  misuse  of,  in  business,  122-123;  points  to  be  considered 
in  use  of,  115-116;  principles  governing  construction  and  use  of, 
119-121. 

Index  number  of  food  prices,  graph  of,  120. 

Investment  facts,  9,  14. 


Labor  facts,  8;  accidents,  16;  classified,  13,  15-18;  compensation  for 
accidents,  16;  immigration,  17-18;  strikes  and  lockouts,  16; 
turn-over,  17;  unemployment,  16-17;  union  membership,  15-16; 
wage-rates  and  earnings,  15. 

Labor  turn-over,  comparability  of  statistics  on,  28. 


INDEX  135 

Land  facts,  11,  23;  classified,  14. 

Law  and  Policy  facts,  14,  24-25. 

Lines,  use  of,  for  comparisons  of  size,  61. 

Logarithmic  charts,  scale  units  and,  59;  (see  "Ratio"  chart). 

M 

Maps,  use  of,  56;  use  of  dot,  62;  use  of  shaded,  63. 

Market,  conditions  affecting,  30-31;  how  to  measure  the,  30-31. 

Market  analysis  by  sampling,  31-32. 

Market  extension  through  business  analysis,  36-37. 

Market  facts,  7,  21-23;  classified,  14;  banking,  21;  commodity  prices, 
22;  credit,  21;  failures,  22;  forecasting,  22-23;  land  and  building, 
23;  money,  21 ;  security  prices,  22;  trade,  21-22. 

Median,  characteristics  of  the,  104-107;  relation  of  the,  to  the  arith- 
metic mean,  106;  how  to  calculate  the,  107. 

Mode,  characteristics  of  the,  108-109;  defined,  107;  relationship  of  the, 
to  the  median,  109;  to  the  arithmetic  mean,  109;  use  of  the,  in 
business  analysis,  109. 

Money,  facts  of,  21. 

Moody  service,  22-23. 

O 

Occupations,  accuracy  of  data  on,  35. 
Office  records,  use  of,  36. 


Pie-diagrams,  to  represent  component  parts  (illustrated),  65-67. 

Population,  distribution  of,  20-21. 

Population  facts,  13,  20-21;  classified,  12. 

Powers  tabulating  machines,  54. 

Price  index  number.  Annalist's,  112;  Bradstreet's,  112;  Bureau  of 
Labor,  112;  Dun's,  112. 

Price  indexes  and  special  use,  112. 

Prices,  commodity,  22;  meaning  of,  111,  116;  methods  and  problems  of 
measurement  of,  111-123;  security,  22;  uses  of  summaries  of, 
111-112. 

Production  facts,  6,  19-20;  classified,  13;  costs,  12;  crops,  19;  manufac- 
tures, 20;  raw  materials,  19-20. 

Production  records,  use  of,  36. 

Profits,  facts  on,  10,  11;  meaning  of  average,  99-100;  measurement  of, 
34. 


136  INDEX 

Q 

Quartiles,  meaning  of  the,  105. 

Questionnaires,  editing  of,  52-53;  principles  in  preparing,  51-52. 

R 

"Ratio"  chart  (illustrated),  93;  characteristics  of  the,  94-96. 
"Ratio"  charts,  contrast  of,  with  difference  charts,  92-96. 
Raw  materials,  mineral,  19-20. 
Research  and  business,  36. 

S 

Sales  campaigns,  population  characteristics  in  developing,  30. 

Sales  facts,  7. 

Sales  records,  use  of,  36. 

Salesmen,  reports  of,  37. 

Salesmanship,  standards  of,  37. 

Sampling,  "law  of  averages"  and,  102-104;  principles  of,  31-32. 

Samples,  requirements  of  good,  103. 

Scale,  horizontal,   in  graphics,   57;    logarithmic,  to    measure    ratio 

changes,  64;  vertical,  in  graphics,   57;  vertical,  in  logarithmic 

charts,  64;  figures,  59;  units,  and  logarithmic  charts,  59;  position 

of,  in  frequency  distributions,  62. 
Scales,  spacings  on  vertical  and  horizontal  (illustrated),  68;  use  of,  in 

graphs  (illustrated),  69. 
Scientific  method,  business  analysis  and,  38-40;  classification  and, 

50;  fact  analysis  and,  36;  meaning  of,  3-4,  8,  12;  phases  of,  in 

business  analysis,  129-130. 
Schedules,  editing  of,  52-53;  principles  in  making,  51-52. 
Secondary  sources,  use  of  data  from,  54. 

Secrist,  Horace,  An  Introduction  to  Statistical  Methods,  58,  122. 
Selling  costs,  business  analysis  and,  36. 
Standardization,  meaning  of,  in  business  statistics,  29. 
Statistical  facts,  must  be  accurate,  34-35;  must  be  comparable,  34; 

must  fit,  33;  must  be  homogeneous,  30-31 ;  must  be  representative, 

31-33;  must  be  stable,  33-34. 
Stock  prices,  measurement  of,  33. 

Strike,  how  measured  statistically,  28;  as  a  statistical  fact,  27-28. 
Surfaces  and  bars  contrasted  (illustrated),  75, 


INDEX  137 

T 

Tables,  preparation  of  useless,  in  business  operations,  54. 

Tabulation,  advantages  of,  41-42;  a  means  not  and  end,  54;  business 
analysis  through,  50;  condensed  detail  and,  48;  contrasted  with 
graphics,  55;  grouping  in,  49;  hand  and  machine,  53-54;  order 
of  detail  in,  43-46;  position  of  totals  in,  46;  principles  to  be  fol- 
lowed in,  43-48;  relation  of,  to  the  collection  of  data,  51,  53; 
relation  of,  to  classification,  41,  53;  titles  to  tables  and,  47-48; 
unclassified  material  and,  50. 

Tax  facts,  11,  14. 

Trade  facts,  21-22. 

Transportation  facts,  23-24;  classified,  14. 

Turn-over,  meaning  of  average,  100;  of  goods,  comparison  of,  31; 
of  labor,  17;  of  labor,  comparisons  of,  31. 


Unemployment,  16-17. 
Union  membership,  15-16. 


U 


w 


Wage,  meaning  of  average,  99. 

Wage-rates,  15. 

Wages,  accuracy  of,  35. 

Wholesale  prices,  measurement  of,  32-33. 

Z 

Zero  line,  marking  of  (illustrated),  69-70;  vertical  scale  and,  86-88. 


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